Desperate or not the answer is YES. It can be done. As long as the right paperwork and channels are used to release the member from his previous Fraternity.
I would make sure that Fraternity B actually is willing to accept member from Fraternity A before he even does this move. It just looks real bad ... no matter what happens.
Loyalty to a certain Organization is of the utmost importance unless they do something that messes with your core belief's.
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