OK, so how do you know if the baptisms for the dead were being conducted under the authority of the church which Jesus established?
Well I have no real reason to think that they were not valid, since Paul does not seem to be condemning the practice. Admittedly it is a single mention of baptism for the dead so not too much detail is provided and I haven’t extensively researched the topic. Jeff Lindsay goes into it in quite some depth:
http://www.jefflindsay.com/LDSFAQ/FQ_BaptDead.shtml#cor