I can think of a few ways to do this:
1) Add the temp's email to the full timer's email client as a second account
2) Setup Bccmode, then either
* setup fetchmail with some rules to pull out items sent by the 'temp' and send them to the full timer
or
* setup mailfilter rules to forward email 'from' tmpuser to fulltimer
(I have not tested this)
3) Use rsync to sync the temp's Sent mail into a folder belonging to the full timer.
I tested the rsync option like this:
* Create a destination folder in the full timer's email in Horde ("Test" in my example)
* Use rsync to copy the mail from tmpuser to fulltimer
export SRCU=tmpuser
export DSTU=fulltimer
export SRCF=.Sent\ Items
export DSTF=.Test
# pre-create the mailbox in fulltimer's email client so that dovecot creates the indexes correctly
# sync the folders that actually contain email
rsync -avz "/home/e-smith/files/users/$SRCU/Maildir/$SRCF/cur/" "/home/e-smith/files/users/$DSTU/Maildir/$DSTF/cur/"
rsync -avz "/home/e-smith/files/users/$SRCU/Maildir/$SRCF/new/" "/home/e-smith/files/users/$DSTU/Maildir/$DSTF/new/"
rsync -avz "/home/e-smith/files/users/$SRCU/Maildir/$SRCF/tmp/" "/home/e-smith/files/users/$DSTU/Maildir/$DSTF/tmp/"
# change the ownership on the copied email files
chown -R $DSTU:$DSTU "/home/e-smith/files/users/$DSTU/Maildir/$DSTF/"
4. I use
Sogo on my server -- I found in Sogo I could 'share' the Sent folder between users. (The wiki page describes the installation of Sogo 3, but Sogo 4 came out a couple years ago...)
It should also be possible to setup Bccmode with 'per user' config -- but I made that suggestion for this problem 5+ years ago and no one ever published notes on exactly how to get it working...