When I was in a Catholic high school in the 60s, we learned that in the case of a Protestant converting to Catholicism, he received "conditional Baptism" -- i.e., "If thou art not already baptized, I baptize thee ..."
“When I was in a Catholic high school in the 60s, we learned that in the case of a Protestant converting to Catholicism, he received “conditional Baptism” — i.e., ‘If thou art not already baptized, I baptize thee ...’”
This seems quite plausible.