Good question. All I know is I have travelled with vehicles that were not in my name (as your VE103 - below - will be) but had letters of permission from the owners (or former keepers). In fact on one bike, I think I may not have even had the original V5. I had no problems at the border, either time.
A convincing looking letter of permission from the leasing agency whose name and address appears on the VE103 will do the trick.
I don't know if they issue such letters as a matter of course, but it needs to link the vehicle listed on the VE103 with your name and address. And if it can be stamped in some way and have a version in French as well as show dates of arrival and departure from Morocco, then so much the better.
Also good will be to do your D16-TER temporary import permit in advance online (as explained here).
That streamlines your passage through immigration; less chance of getting tripped up.
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