Making a mold of a foam latex piece?

I picked up this Mac Tonight "Fingertronic" puppet to use for a project, but being a 30-year-old piece of foam rubber it's beginning to show its age (pic related). What I'd like to do is make a backup copy that I can sculpt on and fix up a bit, then make a plaster mold of that and slip-cast a latex "mask" out of it - I do have a backup plan if all else fails, but is there any way I can make a mold of this piece without causing any more damage to the foam?

I'd recommend 3D scanning it over making a physical mold if you're worried about damaging it. You could easily make a waste mold of the print and clay pour it for adjustments.

If you want to preserve it Tom Spina Designs does absolutely amazing restoration and preservation work.

Do as you would a life cast-use alginate, plaster bandages, clay pour.
Also seal the foam latex with clear acrylic spray beforehand.