I need to store a big message encrypted on a server.
What I am about to do is:

1. Encrypt the message with a AES key;
2. (Authentication) Hash the message with SHA512 and encrypt the hash with RSA priv key (signature);
3. Encrypt AES key, IV and item above with destination RSA public key.

Where HMAC can help?
I have authentication of information and encryption, already, so should I use it?