There is a very recent thread discussing “moving domains between DH accounts”, where a user shares the instructions received from DH support on how to do this, that you might find useful. The “greater thread” in which that post is included also points out the kinds of issues that may be encountered when moving “applications”, so you may (or may not) find the whole thing to be an informative read. You will have some changes to make in the configurations of your Joomla site (to account for the new “paths” that will be involved as you will be running them as a different “user”), and you will have to manage your email addresses as needed. The email address follow the user, not the domain, so the new users will have to set-up email addresses for themselves.
Of course, you could always contact Support yourself, if you wish. Years ago when I did it a few times, DH handled the transferring of the “accounting” and “billing”, but I had to handle my own data transfer. From the recent post I referenced, it looks like that is still the process (see “step 9” in the instruction DH provided the other user). Good Luck!