[CPU] Fix crash issue: RuntimeError: Primitive descriptor was not found for… (#16186)

src/plugins/intel_cpu/src/nodes/matmul.cpp

@@ -624,6 +624,7 @@ void MatMul::prepareParams() {
         primitive_desc_iterator itpd = desc.createPrimitiveDescriptorIterator(engine, key.attr);
         matmul::primitive_desc prim_desc;
 
+        auto itpd_first = itpd;
         while (static_cast<bool>(itpd))  {
             impl_desc_type impl_type = parse_impl_name(itpd.impl_info_str());
 
@@ -631,8 +632,14 @@ void MatMul::prepareParams() {
                 prim_desc = itpd.get();
                 break;
             }
-            if (!itpd.next_impl())
+            if (!itpd.next_impl()) {
-                return matmul();
+                // In case of dynamic shapes an implementation type chosen as optimal for a primitive_desc with
+                // undefined input shapes, is not necessarily available for the primitive_desc with defined shape.
+                // Example: brgemm_avx512_amx (Intel Sapphire Rapids Platform) is available for a primitive with
+                // undefined input shapes but not available for primitive_desc with input batch 1.
+                prim_desc = itpd_first.get();
+                break;
+            }
         }
         return matmul(prim_desc);
     };

src/plugins/intel_cpu/tests/functional/single_layer_tests/matmul.cpp

@@ -1277,6 +1277,13 @@ INSTANTIATE_TEST_SUITE_P(nightly_MM_Brgemm_Amx_Static, MatMulLayerCPUTest, testB
 
 
 const std::vector<ShapeRelatedParams> IS_Brgemm_Dynamic = {
+        {
+                {
+                        {{-1, 256}, {{1, 256}}},
+                        {{256, 384}, {{256, 384}}}
+                },
+                {false, false}
+        },
         {
                 {
                         {{-1, -1}, {{55, 12}, {33, 7}}},