the common approach is to store the old password hash in the new schema. at login if the old hash is not null, compute the hash from the password and compare. if a match, clear the old ash, and update the password (compute) the new hash.
if you do not have code to compute the hash, then you a conversion flag, if set, call a web service on the old site, that validates the user/password. if valid update the password on the new system.
if you scaffold the razor login page, you can make the required changes.