Hmmm. That is what I was saying too, that “simple convalidation” is not possible in this case. But I wrote, because cannon 1157 requires that both must acknowledge it was null from the beginning, and he could not truthfully agree. It is not clear why he would agree to a new marriage when he believes he is already in one, but maybe there is a misunderstanding of what a convalidation is.
I was in this same situation. It should be very easy to receive a Radical Sanation because the catholic husband married a non baptized person outside the Church, not knowing he needed a dispensation. That was my situation exactly. Once I explained to the priest that my wife didn’t want a convalidation because she felt we were validly married and that I thought that we were good and believed that we both gave consent, it was easy for the priest to write up the application and the Archbishop signed it without any questions.
To the OP, if you have any issues, please feel free to contact me via PM.