The recent security problems have nothing to do with which hash function is used.
That being said you'd need to re-write the login system to use a sha-256 scheme including adding in a javascript library that will do the sha hashing on the client side. Additionally there would be encoding considerations to take into account in that you'd have to make sure that the character encoding of the password is maintained between the two forum softwares. There are probably other issues as well.
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