If you are wanting to take your skull home for a euro mount, read the cwd regulation. If still unsure I suggest calling Brian Nesvick or his replacement Rick King, the new chief game warden/Division Chief, and ask.
Per 2019 regulation, it is not illegal to take the head of Elk/Deer/Moose out of wyoming, nor are you required to cut the skull cap off. Cape it, remove the eyes and brains, and you're fine. Wyoming added "skull" to their regulation, allowing you to do a euro mount at home. Some neighboring states however, have not included the work "skull" in their regulation so getting the skull back into your state may still be a problem but I'd call and ask them as well.
Incorrect. Per 2019 regulation brochure, page 5, only certain parts of elk, deer, or moose may be transported to other states or countries. That excludes the head with brain matter intact, spinal column or teeth.
I delivered a quite a bit of Game and Fish records to Brian before they went all digital. The recommendation to call the chief game warden or the licensing staff at WGFS is a good one. Phone numbers are on page 2 of your brochure. I work with the State Records Center and deal with a quite a few of these regulations and related files. My advice comes through calls I made to the Licensing Desk to be sure along with the regional office for the Gillette and Cheyenne areas who I always call before I go hunting. Next year I am planning to hunt areas 104/102 on a general license so I will be contacting the regional warden for those areas to get advice on specific restrictions and requirements. Be aware that the brochure IS NOT the regulation, it is for information only. You still have the duty to know and obey the law. Actual game commissioner signed regulations are posted on the WGFS website.
EDIT: I made the call to the G&F to be sure. You can take head and antlers out of state provided all meat, brain matter and teeth are removed. It is tricky, but you CAN remove the skin from the head for a taxidermy mount. Personally, I recommend finding an instate taxidermist who can ship your mount to you and ask how they want the hide prepared.
Cut and paste directly from Page 5 of the 2019 Hunting Brochure: "Deer, elk or moose taken from within any other state, province or country may only be imported into Wyoming if carcasses are transported directly to a private residence for processing, to a taxidermist, to a processor or to a CWD sample collection site provided the head and all portions of the spinal column are disposed of in an approved landfill or incinerator. " and for transportion within the State of Wyoming for animals killed in this state: "a) Deer, elk and moose taken in Wyoming may be transported within Wyoming to a camp, a private residence for processing, a taxidermist, a processor, or a CWD sample collection site in Wyoming, provided the head and all portions of the spinal column remain at the site of the kill or such parts are disposed of in any approved landfill or approved incinerator in Wyoming."
Now read the last sentence completely. You can transport a head directly to a taxidermist or to your home in Wyoming BUT you must dispose of the viscera and bones and spinal column and that in an approved landfill. Most cities I know of take that into their trash collection and dispose of it in an approved landfill.