Birkin took over Marcus' work in the late 70's. James Marcus founded the Umbrella Corporation with Spencer in the 1950's and created the Progenitor Virus, which became the T-Virus after he mixed it with leech DNA.
Birkin advanced the T-Virus, but he absolutely did not create it. Excerpts from Resident Evil Zero as prooof:
Marcus' Diary 1
December 4th
We finally did it....the new virus! We have called it the "Progenitor". I want to carry it back and start detailed invesgations immediately.
September 19th
At last...I've discovered a way to build a new virus type with "Progenitor" as a base. Mixing it with leech DNA was a breakthrough I needed.. I call this new virus "T", for "Tyrant".