This is the approved revision of this page, as well as being the most recent.
Doing a System Transfer with homebrew is possible, but titles that were not downloaded from the eShop will temporarily disappear at the end.
Does the target console have custom firmware?
Yes
No
It is highly recommended that you set up CFW first using 3DS Hacks Guide. This will make it easier to restore software after the transfer.
FAQ
Is setting up CFW first really required?
Strictly speaking it is not. In this case any software that was not purchased and downloaded from Nintendo eShop will be invisible and not fixable until CFW is installed.
Since it is more convenient and sometimes easier to set up custom firmware on a freshly-formatted console, it is recommended to set it up first.
Is there a workaround for the 7-day cooldown?
No, this is enforced server-side.