If your ex- uses the insurence

then both of you commit insurence fraud. If the insurence company
finds out about it, the minimum punishment is for you to pay back
all the covered amount. The insurence company can also pursue criminal
punishment depending on the amount involved.

One thing you might want to look at is whether your company's
health insurence covers "cohabit couple". Your ex and you can be
divorced and cohabit, so you may be able to use the coverage.