Your method for storing the passwords server-side is actually not very secure. Hashing the passwords without a unique salt is not a secure way to store them.
For one thing, every user with the password of 'secret' will have the same hash in your database. Secondly, if I were to steal all of your password hashes, I would just have to compute sha2 of every 6-8 (or whatever password length you are using) character string. With a 32 character salt, I would have to compute a sha2 of every 38-40 character string, making my job a more time consuming.
You can't have it both ways. If you are hashing the password before it is sent from the client to the server, you need the raw password on the server side.
(Assuming you are concatenating it with a server-provided random value before the hashing.)
For one thing, every user with the password of 'secret' will have the same hash in your database. Secondly, if I were to steal all of your password hashes, I would just have to compute sha2 of every 6-8 (or whatever password length you are using) character string. With a 32 character salt, I would have to compute a sha2 of every 38-40 character string, making my job a more time consuming.