Will this update older MD5 (not PHPass) hashes on login?

I have a situation where I need to backload MD5 hashes into a WordPress site directly (updates are processed on an external system, and the MD5 hashed passwords passed via WebHook – we don’t get the plain text password). My understanding was the user should be able to login with their password if only the basic MD5 hash was stored in the database, and WordPress would update that on login to PHPass and reserve the new hash for future logins, but that doesn’t seem to work anymore. The login doesn’t throw an error, it just refreshes and doesn’t proceed to the logged in profile page.

Will your plugin recognize those old MD5 hashes, validate the login and generate a new password hash and store that in the database? Thanks!