This sounds like a slight modification of common support software that generates trouble tickets. I researched this several years ago for a client and there were a lot of products available. The good ones would work on a network and allow an operator to take a phone call, open up a new trouble ticket, forward it to the appropriate people, etc. The tickets would remain open until the problem was resolved. Also, a history is kept of all transactions with the customer. If that customer calls in the future, you can type in his or her name, and once verified have a record of every phone call or E-mail they’ve sent to the company, along with what was done for them. So if they say they still can’t get something to work the operator can instantly respond, “Well, it says that James B. solved your problem for you and notified you of a fix on April 13. Let me forward you to James.”
I’d be surprised if such products didn’t support E-mail contacts now.
To find them, search the internet for “Help Desk Software”, “Trouble Tickets” “Customer Support Software”, etc.