I don't read the sentences as completely equivalent, the sentence (A) expresses a dependence on how genuine he feels he can be and both vulnerability and strength, while sentence (B) expresses a relation between vulnerability more clearly than it does to strength.
I read the first sentence as ability to be more genuine = more vulnerability + more strength.
The second sentence as ability to be more genuine = more vulnerability + he will take singular action to be stronger.
If you would want to imply the same meaning, I would use.:
As he feels that he can be more genuine with you, he'll be free to express more of his vulnerability and will become stronger because of it.