It would be easier to do the entire mask than to make two pieces and try to fasten them together.

If the original mask is one of those that are commonly seen in craft shops, I think you could apply the papier mache directly to it, as PM doesn't stick too well to plastic when it's dry -- you can usually pop it off (as long as you didn't wrap any around the edges).  But trying just a lump as David suggested could be a good idea, just to make sure, and then follow the rest of his directions.

"...regarding the best method to use in order to try and capture as many details from the original mask as possible..."

Are you speaking of duplicating a FINISHED mask that was built on top of a plastic form?  Or a formed all-plastic mask such as B, below?

A) Basic plastic mask:  https://www.amazon.com/Creativity-Stree … B00A6VYL4O
B) Molded plastic mask: https://unboundart.deviantart.com/art/D … -121699614
C) Built-up handmade mask:  https://www.google.com/search?hl=en& … 4935427238

If B, it should be no more of a problem than A, but when you're laying the strips, press them firmly into the depressed areas.

If C, you will have to use Saran Wrap (Clingfilm), and then start from the center and work your way to the edges, carefully. Even then, after you remove it from the mold, you will have to clean up any places where the plastic film folded or wrinkled.

If you have or are making a mask that you want to DUPLICATE, we would be talking about MOLDMAKING, and you would want to use the original as a Form, cover with plastic film, and build a Mold over it.  When it's dry, you would remove the original, and build your papier mache mask inside the mold to Duplicate all of the details.

This kind of mask is the most difficult to duplicate; if there is even one undercut (like a long, hooked nose), you won't be able to remove the duplicate from the mold without tearing it to pieces.

Molds are often made of plaster, or non-drying clay (Plasticine in the U.S.), or clays that do harden, but aren't fired in a kiln.

If using non-hardening (oil-based) clay, most of them have enough oil in them that they will separate from the new creation, but adding a bit of petroleum jelly won't hurt. 

If using a porous mold (plaster, drying clay, etc), when it is completely dried or cured, you will need to line it with Zinsser Bulls Eye brand spray shellac (this is a true shellac and not a synethic polyurethane) and let it dry, so the papier mache glue doesn't seep into the tiny holes (then you'll never separate it from the mold).

And then when ready to use, you must apply a thin coating of petroleum jelly or mineral oil (baby oil type, not tool oil type) before you start applying your papier mache.

Moldmaking is an art in itself, so do some research before you decide go in that direction.

Sue