If the 1:1 relationship with total participation is the only relationship between the two entities, you just merge them into a single relation. The choice of the primary key will be arbitrary (pick one of the PK of the original entities, while the other PK will be an alternate key).
If instead there are additional relationships between the two entities, which prevent the merge into a single relation, you can treat the entities as in a parent-child relationship, and the choice of where to put the foreign key is arbitrary.