The converse can be used of course to prove equivalences, since is
Here are two links talking about some uses of the converse :
Converse, Inverse, Contrapositive
Logic - Converse
If you look at the second link, you can see that there's no direct relation between the truth table of the implication and the one of the converse.
Right now, I can't remember using the converse to prove anything... Maybe I did...