As per the bounce-back message - the inbox was full and needs to be increased via CPanel
But for a long term solution, I would highly recommend a switch to the likes of G-suite where the minimum use email is 15-30GB whereas a server can not generally hold that amount of email. It's dedicated email and is much more
G-Suite is a paid dedicated service - like anything, you get what you pay for but have a look at G-Suite anyway - I recommend all users of higher level email, to transfer to G-Suite.
It's a long term and much preferred solution and I do have a Google Provider who can assist in that if/when ready - it would also include saving data in the cloud and syncing etc.