diff --git a/.github/workflows/codespell.yml b/.github/workflows/codespell.yml
index 6c48a057f..5542a0e59 100644
--- a/.github/workflows/codespell.yml
+++ b/.github/workflows/codespell.yml
@@ -5,4 +5,4 @@ jobs:
     runs-on: ubuntu-latest
     steps:
     - uses: actions/checkout@v4
-    - uses: codespell-project/actions-codespell@v2.0
+    - uses: codespell-project/actions-codespell@v2.1
diff --git a/doc/attr.xml b/doc/attr.xml
index 986827a8c..284510215 100644
--- a/doc/attr.xml
+++ b/doc/attr.xml
@@ -1292,7 +1292,7 @@ true]]></Example>
 
     <C>NambooripadPartialOrder</C> returns the Nambooripad partial order on the
     regular semigroup <A>S</A> as a list of sets of positive integers where
-    entry <C>i</C> in <C>NaturalPartialOrder(<A>S</A>)</C> is the set of
+    entry <C>i</C> in <C>NambooripadPartialOrder(<A>S</A>)</C> is the set of
     positions in <C>Elements(<A>S</A>)</C> of elements which are less than
     <C>Elements(<A>S</A>)[i]</C>. See also <Ref
       Func="NambooripadLeqRegularSemigroup"/>.
diff --git a/etc/code-coverage-test-gap.py b/etc/code-coverage-test-gap.py
index e50ea5a89..f52bbdf31 100755
--- a/etc/code-coverage-test-gap.py
+++ b/etc/code-coverage-test-gap.py
@@ -64,19 +64,29 @@
 _DIR = tempfile.mkdtemp()
 print(f"{_INFO_PREFIX}Using temporary directory: {_DIR}\033[0m")
 
-_COMMANDS = 'echo "'
-_COMMANDS += "".join(rf"Test(\"{f}\");;\n" for f in _ARGS.tstfiles)
-_COMMANDS += rf"""UncoverageLineByLine();;
-LoadPackage(\"profiling\", false);;
-filesdir := \"{getcwd()}{_PROFILE_DIR}\";;\n"""
-
-_COMMANDS += rf"outdir := \"{_DIR}\";;\n"
-_COMMANDS += rf"x := ReadLineByLineProfile(\"{_DIR}/profile.gz\");;\n"
-_COMMANDS += 'OutputAnnotatedCodeCoverageFiles(x, filesdir, outdir);"'
+# Raw strings are used to correctly escape quotes " for input in another
+# process, i.e. we explicitly need the string to contain \" instead of just "
+# for each quote.
+_GAP_COMMANDS = [rf"Test(\"{f}\");;" for f in _ARGS.tstfiles]
+_GAP_COMMANDS.extend(
+    [
+        "UncoverageLineByLine();;",
+        rf"LoadPackage(\"profiling\", false);;",
+        rf"filesdir := \"{getcwd()}{_PROFILE_DIR}\";;",
+        rf"outdir := \"{_DIR}\";;",
+        rf"x := ReadLineByLineProfile(\"{_DIR}/profile.gz\");;",
+        "OutputAnnotatedCodeCoverageFiles(x, filesdir, outdir);",
+    ]
+)
 
 _RUN_GAP = f"{_ARGS.gap_root}/gap -A -m 1g -T --cover {_DIR}/profile.gz"
 
-with subprocess.Popen(_COMMANDS, stdout=subprocess.PIPE, shell=True) as pro1:
+# Commands are stored in a list and then joined with "\n" since including
+# newlines directly in raw strings cause issues when piping into GAP on some
+# platforms.
+with subprocess.Popen(
+    'echo "' + "\n".join(_GAP_COMMANDS) + '"', stdout=subprocess.PIPE, shell=True
+) as pro1:
     try:
         with subprocess.Popen(_RUN_GAP, stdin=pro1.stdout, shell=True) as pro2:
             pro2.wait()
diff --git a/gap/attributes/isomorph.gi b/gap/attributes/isomorph.gi
index 5d28954a8..c785ec0eb 100644
--- a/gap/attributes/isomorph.gi
+++ b/gap/attributes/isomorph.gi
@@ -105,7 +105,65 @@ end);
 
 InstallMethod(IsIsomorphicSemigroup, "for semigroups",
 [IsSemigroup, IsSemigroup],
-{S, T} -> IsomorphismSemigroups(S, T) <> fail);
+function(R, S)
+  local uR, uS, map, mat, next, row, entry, isoR, rmsR, isoS, rmsS;
+
+  if not (IsFinite(R) and IsSimpleSemigroup(R)
+          and IsFinite(S) and IsSimpleSemigroup(S)) then
+    return IsomorphismSemigroups(R, S) <> fail;
+  fi;
+
+  # Note that when experimenting the method for IsomorphismSemigroups for Rees
+  # 0-matrix semigroups is faster than the analogue of the below code, and so
+  # we do not special case finite 0-simple semigroups.
+
+  # Take an isomorphism of R to an RMS if appropriate
+  if not (IsReesMatrixSemigroup(R) and IsWholeFamily(R)
+      and IsPermGroup(UnderlyingSemigroup(R))) then
+    isoR := IsomorphismReesMatrixSemigroupOverPermGroup(R);
+    rmsR := Range(isoR);
+  else
+    rmsR := R;
+  fi;
+  # Take an isomorphism of S to an RMS if appropriate
+  if not (IsReesMatrixSemigroup(S) and IsWholeFamily(S)
+      and IsPermGroup(UnderlyingSemigroup(S))) then
+    isoS := IsomorphismReesMatrixSemigroupOverPermGroup(S);
+    rmsS := Range(isoS);
+  else
+    rmsS := S;
+  fi;
+
+  if Length(Rows(rmsR)) <> Length(Rows(rmsS))
+      or (Length(Columns(rmsR)) <> Length(Columns(rmsS))) then
+    return false;
+  fi;
+
+  uR := UnderlyingSemigroup(rmsR);
+  uS := UnderlyingSemigroup(rmsS);
+
+  # uS and uR must be groups because we made them so above.
+  map := IsomorphismGroups(uS, uR);
+  if map = fail then
+    return false;
+  fi;
+
+  # Make sure underlying groups are the same, and then compare
+  # canonical Rees matrix semigroups of both R and S
+  mat := [];
+  for row in Matrix(rmsS) do
+    next := [];
+    for entry in row do
+      Add(next, entry ^ map);
+    od;
+    Add(mat, next);
+  od;
+
+  rmsR := CanonicalReesMatrixSemigroup(rmsR);
+  rmsS := ReesMatrixSemigroup(uR, mat);
+  rmsS := CanonicalReesMatrixSemigroup(rmsS);
+  return Matrix(rmsR) = Matrix(rmsS);
+end);
 
 InstallMethod(IsomorphismSemigroups, "for finite simple semigroups",
 [IsSimpleSemigroup and IsFinite, IsSimpleSemigroup and IsFinite],
diff --git a/gap/attributes/isorms.gi b/gap/attributes/isorms.gi
index 60e6e75b9..16eb327f8 100644
--- a/gap/attributes/isorms.gi
+++ b/gap/attributes/isorms.gi
@@ -1368,7 +1368,7 @@ function(S)
 end);
 
 InstallMethod(CanonicalReesMatrixSemigroup,
-"for a Rees 0-matrix semigroup",
+"for a Rees matrix semigroup",
 [IsReesMatrixSemigroup],
 function(S)
   local G, mat;
diff --git a/tst/standard/attributes/isomorph.tst b/tst/standard/attributes/isomorph.tst
index 92d9ae609..428e3dd2d 100644
--- a/tst/standard/attributes/isomorph.tst
+++ b/tst/standard/attributes/isomorph.tst
@@ -9,7 +9,7 @@
 ##
 
 #@local A, BruteForceInverseCheck, BruteForceIsoCheck, F, G, S, T, U, V, inv
-#@local map, x, y
+#@local map, x, y, M, N, R, L
 gap> START_TEST("Semigroups package: standard/attributes/isomorph.tst");
 gap> LoadPackage("semigroups", false);;
 
@@ -118,6 +118,44 @@ gap> T := JonesMonoid(4);
 gap> IsIsomorphicSemigroup(S, T);
 false
 
+# isomorph: IsIsomorphicSemigroup, for finite simple semigroups
+gap> M := [[(1, 2, 3), ()], [(), ()], [(), ()]];
+[ [ (1,2,3), () ], [ (), () ], [ (), () ] ]
+gap> N := [[(1, 3, 2), ()], [(), (1, 2, 3)], [(1, 3, 2), (1, 3, 2)]];
+[ [ (1,3,2), () ], [ (), (1,2,3) ], [ (1,3,2), (1,3,2) ] ]
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), M);
+<Rees matrix semigroup 2x3 over Alt( [ 1 .. 3 ] )>
+gap> S := ReesMatrixSemigroup(Group([(1, 2, 3)]), N);
+<Rees matrix semigroup 2x3 over Group([ (1,2,3) ])>
+gap> IsIsomorphicSemigroup(R, S);
+true
+gap> R := SemigroupByMultiplicationTable(MultiplicationTable(R));;
+gap> S := SemigroupByMultiplicationTable(MultiplicationTable(S));;
+gap> IsIsomorphicSemigroup(R, S);
+true
+gap> L := [[(), ()], [(), ()], [(1, 2, 3), ()]];
+[ [ (), () ], [ (), () ], [ (1,2,3), () ] ]
+gap> T := ReesMatrixSemigroup(SymmetricGroup([1 .. 3]), L);
+<Rees matrix semigroup 2x3 over Sym( [ 1 .. 3 ] )>
+gap> IsIsomorphicSemigroup(S, T);
+false
+gap> IsIsomorphicSemigroup(T, T);
+true
+gap> M := [[(1, 2, 3), ()], [(), ()], [(), ()]];
+[ [ (1,2,3), () ], [ (), () ], [ (), () ] ]
+gap> N := [[(1, 3, 2), ()], [(), (1, 2, 3)]];
+[ [ (1,3,2), () ], [ (), (1,2,3) ] ]
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), M);;
+gap> S := ReesMatrixSemigroup(AlternatingGroup([1 .. 3]), N);;
+gap> IsIsomorphicSemigroup(R, S);
+false
+gap> R := ReesMatrixSemigroup(AlternatingGroup([1 .. 5]),
+> [[(), ()], [(), (1, 3, 2, 4, 5)]]);;
+gap> S := ReesMatrixSemigroup(AlternatingGroup([1 .. 5]),
+> [[(1, 5, 4, 3, 2), ()], [(1, 4, 5), (1, 4)(3, 5)]]);;
+gap> IsIsomorphicSemigroup(R, S);
+false
+
 # isomorph: IsomorphismSemigroups, for infinite semigroup(s)
 gap> S := FreeSemigroup(1);;
 gap> T := TrivialSemigroup();;