diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index fe77b50fcfd..9f0eb992c13 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -940,10 +940,22 @@ def __mul__(self, other):
             sage: WordMorphism('')*m
             Traceback (most recent call last):
             ...
-            KeyError: 'b'
+            ValueError: the codomain alphabet of the second morphism must be included in the domain alphabet of the first morphism with the same ordering
             sage: m * WordMorphism('')
             WordMorphism:
-        """
+            sage: s = WordMorphism('a->ba,b->a', domain=Words('ab'), codomain=Words('ba'))
+            sage: s * s
+            Traceback (most recent call last):
+            ...
+            ValueError: the codomain alphabet of the second morphism must be included in the domain alphabet of the first morphism with the same ordering
+        """
+        # Check that other's codomain alphabet is included in self's domain alphabet
+        # with the correct ordering
+        if not self._is_alphabet_included_with_order(
+                other.codomain().alphabet(), self.domain().alphabet()):
+            raise ValueError("the codomain alphabet of the second morphism must be "
+                           "included in the domain alphabet of the first morphism "
+                           "with the same ordering")
         return WordMorphism({key: self(w) for key, w in other._morph.items()},
                             codomain=self.codomain())
 
@@ -982,7 +994,7 @@ def __pow__(self, exp):
             sage: n^2
             Traceback (most recent call last):
             ...
-            KeyError: 'c'
+            ValueError: the codomain alphabet of the second morphism must be included in the domain alphabet of the first morphism with the same ordering
         """
         # If exp is not an integer
         if not isinstance(exp, (int, Integer)):
@@ -1203,9 +1215,88 @@ def is_endomorphism(self):
         """
         return self.codomain() == self.domain()
 
+    def _is_alphabet_included_with_order(self, source_alphabet, target_alphabet):
+        """
+        Check if ``source_alphabet`` is included in ``target_alphabet`` with the correct ordering.
+
+        This is a helper function for checking composition validity.
+        For composition ``self * other`` to preserve the incidence matrix
+        property, we need ``other.codomain().alphabet()`` to be included
+        in ``self.domain().alphabet()`` with matching order.
+
+        INPUT:
+
+        - ``source_alphabet`` -- the alphabet to check for inclusion
+        - ``target_alphabet`` -- the alphabet to check inclusion into
+
+        OUTPUT:
+
+        ``True`` if all letters of ``source_alphabet`` appear in
+        ``target_alphabet`` in the same relative order, ``False`` otherwise.
+
+        EXAMPLES::
+
+            sage: m = WordMorphism('a->ab,b->a')
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('ab').alphabet(), Words('ab').alphabet())
+            True
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('ab').alphabet(), Words('abc').alphabet())
+            True
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('ba').alphabet(), Words('ab').alphabet())
+            False
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('ba').alphabet(), Words('abc').alphabet())
+            False
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('ac').alphabet(), Words('abc').alphabet())
+            True
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('abc').alphabet(), Words('abc').alphabet())
+            True
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('abc').alphabet(), Words('ab').alphabet())
+            False
+            sage: m._is_alphabet_included_with_order(
+            ....:     Words('').alphabet(), Words('ab').alphabet())
+            True
+        """
+        # Check if alphabets are equal first (fast path)
+        if source_alphabet == target_alphabet:
+            return True
+
+        # Check cardinality constraints
+        if target_alphabet.cardinality() < source_alphabet.cardinality():
+            return False
+
+        if target_alphabet.cardinality() == Infinity:
+            raise NotImplementedError("cannot check alphabet inclusion for infinite alphabets")
+
+        # Check that all letters in source_alphabet are in target_alphabet
+        source_list = list(source_alphabet)
+        target_list = list(target_alphabet)
+
+        if not all(a in target_alphabet for a in source_list):
+            return False
+
+        # Check that the relative order is preserved
+        # Find positions of source letters in target
+        target_positions = {letter: i for i, letter in enumerate(target_list)}
+        source_positions = [target_positions[letter] for letter in source_list]
+
+        # Check if positions are in increasing order
+        return all(source_positions[i] < source_positions[i+1]
+                   for i in range(len(source_positions)-1))
+
     def is_self_composable(self):
         r"""
-        Return whether the codomain of ``self`` is contained in the domain.
+        Return whether the codomain of ``self`` is contained in the domain
+        with the correct ordering.
+
+        For a morphism to be self-composable (i.e., ``self * self`` to be valid),
+        the codomain alphabet must be included in the domain alphabet with the
+        same relative ordering of letters.
 
         EXAMPLES::
 
@@ -1214,16 +1305,16 @@ def is_self_composable(self):
             False
             sage: f.is_self_composable()
             True
+
+        Check that alphabet ordering matters::
+
+            sage: s = WordMorphism('a->ba,b->a', domain=Words('ab'), codomain=Words('ba'))
+            sage: s.is_self_composable()
+            False
         """
         Adom = self.domain().alphabet()
         Acodom = self.codomain().alphabet()
-        if Adom == Acodom:
-            return True
-        if Adom.cardinality() < Acodom.cardinality():
-            return False
-        if Adom.cardinality() == Infinity:
-            raise NotImplementedError
-        return all(a in Adom for a in Acodom)
+        return self._is_alphabet_included_with_order(Acodom, Adom)
 
     def image(self, letter):
         r"""