How to make two TopoDS_Shapes equal after deserializing with BRepTools::Read?

I have two solids that were processed with BRepAlgoAPI_MakeConnected. After the operation, some of their faces should be topologically identical—i.e., they should compare as IsEqual (or at least IsSame).

However, when I serialize each solid separately using BRepTools::Write and then deserialize them back with BRepTools::Read, the corresponding faces are no longer IsEqual—even though they originated from the same connected geometry.

I understand that deserialization creates new TShape instances, so pointer-based identity is lost. But is there a way to preserve or restore the topological equivalence so that IsEqual (or IsSame) returns true for the matching faces?

Or, more generally: what’s the recommended approach to reliably identify “the same” sub-shapes across independently deserialized copies of a shape?