The phrase 'while assigned to' is correct and usable in written English.
You can use it to connect one clause to another, to indicate that something happened or was happening during a particular time period, or to indicate that something is related to a particular task or job. For example, "I worked on the project while assigned to the accounting department."
While assigned to head the arts and entertainment section, he remains a managing editor.
While assigned to Lummus Spain, Sven met and married Jytte Engel-Andreasen.
The agent and a colleague were kidnapped in 2009 while assigned to the international effort to assist Somalia's transitional government in Mogadishu.
While assigned to police headquarters for The New York Evening Post, Steffens heard a great yarn about a robbery, and wrote about it.
A 51-year-old firefighter broke his leg last night while assigned to the cleanup and recovery effort at ground zero.
He volunteered to the K.G.B. while assigned to the F.B.I.'s intelligence division in New York, where he was a supervisor of a counterintelligence squad.
The shooting occurred while Officer Ryan, assigned to the Fifth Precinct, was on patrol with another officer and a sergeant.
While patents assigned to non-profit organizations (incl. individual ownership of the professors themselves) complement publication quantity and quality, patents assigned to corporations are negatively related to quantity and quality of publication output.
In addition, National Guard military police have been helping to beef up security at Fort Dix, while police assigned to the Air National Guard's 108th Air Refueling Wing provided added security to McGuire Air Force Base before being reassigned to patrol sites in Washington, said Colonel Dwyer.
An occasional fat bonus or raise fills in the blanks for positive feedback, while being assigned to "special" projects — projects that go nowhere — might signal it's time to move on.
While initially assigned to the Baltic Fleet, the ship was detached to the Mediterranean several times before the start of World War I in 1914.
