"while in the process" is a grammatically correct phrase and it can be used in written English.
It is typically used to indicate that an action or event is occurring at the same time as another action or event. Example: While in the process of cooking dinner, I received a phone call from my friend.
DiskJokke recorded it while in the process of splitting up with his long-term girlfriend – and eventually leaving her and their baby daughter.
It is breathtaking and beautiful seeing such men create their own styles while in the process chasing down the records of the great goal scorers.
In 1914 he had surgery for the removal of his appendix, and, while in the process of recovery, he committed suicide.
In the same year, he was arrested in Algiers by the French military authorities while in the process of negotiating peace terms with the French premier, Guy Mollet.
Transgender individuals who resort to unprescribed hormones while in the process of changing their sex risk infection and other side effects.
"Must rush or the Astors and Vanderbilts will think I'm not coming," he writes teasingly from New York in 1921, while in the process of taking that city by storm and sending the good news home to England.
While in the multistage processes, the process in each stage is affected by the processes in the previous stages.
We have never had a seizure, convulsion or spasm while engaged in the process of communication.
It was the most revolting concoction imaginable, yet we downed it in swift, greedy gulps, dead drunk while still in the process of drinking.
This means that during its first five-year term, while still in the process of rotating in political allies, a Chinese administration is essentially a lame duck.
If the participant needs support at the workplace, the participant may receive five additional sessions of coaching while being in the process of RTW.
