Just to add my 2¢, I can't positively identify your rifle, but I agree with the consensus that it is representative of a Hawken full stock rifle.
I own a GRF NW trade gun and a GRF Hudson's Bay Factor's Pistol, both of which were made when Frank Straight owned the company. I have also researched the company from the old black powder magazines and through their catalogs.
Green River Forge went through three different ownerships. Frank Straight started the company in Bellevue, Washington in the late 1960's or early 1970's. Straight sold the business in early 1977, and it was moved to Springfield, Oregon. A Herb Hazen, Bill Jones, and Jess Scott appear to have operated the company in Springfield. Green River Forge was sold again at the end of 1979 and moved to Roosevelt, Utah, the home of GRRW. The new owner was Bill Brandenburg, the business manager of Green River Rifle Works.
Bill Brandenburg may have bought GRF as a life line because of the financial trouble GRRW was having and knew its days were numbered. He operated GRF out of Roosevelt, Utah until early 1985 when he moved to California.
From GRF Catalog used in 1976 when Frank Straight still owned the company.
From GRF Catalog used in 1979 when the company was in Springfield, Oregon.
From GRF Catalog used in 1980 when the company was in Roosevelt, Utah.
1980 GRF Price List
GRF Catalog used in 1984/85
Frank Straight only lists the NW Trade Gun, the Astorian Rifle, and the Hudson's Bay Factor's Pistol when he owned the company.
The Springfield, Oregon company added the Oregon Territory Rifle to the line.
Brandenburg lists the same guns in his first catalog and price list as shown above, but by 1985 he was only listing the NW Trade Gun and the Factor's Pistol as finished guns. It doesn't appear that Brandenburg made very many guns while he owned the company as he seems to have focused on expanding the line of Period Clothing Patterns and the sale of books. I've yet to see a GRF gun known to have been made by Brandenburg or someone in his employ, but they may be out there.
That said, Mike's full stock Hawken may have been made by Brandenburg as a special order item. I agree with
Hungry Horse that this rifle would have to be a late production item. I don't see any characteristics that would suggest it was made when Straight owned the company or when the company was located in Springfield, Oregon.
It has been pointed out that the trigger guard is similar to those used by GRRW on their Hawken rifles. I agree with this, though that guard was commercially available from a number of suppliers back then. A little more telling, the butt plate on the subject rifle was also used on GRRW's full stock Hawken rifles. It is the same butt plate that GRRW used on their "Bridger" pattern rifles and may have been a propriety butt plate as we don't see it available commercially again until 1986 when TOTW began offering their "Bridger Hawken" using GRRW's original stock pattern and other parts provided them by Dr. Gary White.
The last bit of circumstantial evidence is the caliber and "GRF" stamps are located on the same flat near the breech that GRRW usually stamped their guns with the caliber, serial number, and makers mark.
None of this is definitive, but it does have enough similarities to GRRW's rifles to suggest that Brandenburg may have made it.
That's assuming of course that the stamp on the barrel stands for Green River Forge and not some individual's initials.