"Don't you have it in your mail program?"
No; he deletes emails as he is done with them.
Take a close look at your hard drive.
Your mailbox is one of the smallest large files on your hard drive, and your hard drive is less than 25% full anyway.
Consider, within your email client (Mozilla Thunderbird, Eudora, Outlook etc.) creating a folder each month. Name it with the year and month, thus "Trash_201001" for January this year, "Trash_200912" for December last year, and drag your completed emails into the corresponding trash folder.
You can ask your email client program to search the trash folder(s) by to, from, subject, text body, date and so on in unlimited combinations and reduce your head-scratching time from hours to seconds.
Computers are designed to perform boring and menial tasks, freeing our brains up for the creative stuff.