I'm sorry for the loss of your tiel and that Charlie is missing his friend.
It's best not to get a mirror as this can confuse and cause behaviours not wanted in solo bird friends.
When you are gone during those 4-5 hours make sure you leave the TV or some music on for Charlie.
When you are home, try and send some extra time near to him, talking to him and playing with him if he is tame.
It's important not to rush in to replacing Charlie's friend.
Let Charlie grieve first. Having had a pair that were very close before and losing one, I know how hard a bird can take the loss of a friend- even having other birds to keep him company.
You are the only one who knows how close they are, so you are the best person to judge how well Charlie is doing.
When you feel that Charlie is more like himself, you can consider getting a new budgie friend for him.
Hopefully you have a spare cage to keep a new bird in during quarantine.
Quarantine IS Necessary!
After the quarantine process, you can look at introducing them into the same room, and eventually let them meet.
Introducing Two Budgies