The phrase "a process of his" is correct and usable in written English.
It can be used to refer to a specific process that belongs to or is associated with a male individual.
Example: "The success of the project was largely due to a process of his that streamlined the workflow."
Alternatives: "his method" or "his approach".
During the deliberations surrounding the establishment of a new government, Nasser began a process of sidelining his rivals among the original Free Officers, while elevating his closest allies to high-ranking positions in the cabinet.
Such a repertoire is fluid, and if in recent years it has undergone a "process of codification," his approach can't help but be subjective, defined by his experience and sensibility.
He would then have to go through a process of rebuilding his strength and conditioning.
With a background in graphic design, Gilley has created a process of translating his works from the digital stage, using Illustrator and Photoshop, to the physical presentation using projections to hand craft his installations. .
In this as in other aspects of his thought, he seemed in a process of rising above his cultural environment.
He was very good with the ball, he fitted the philosophy perfectly and defensively he was exceptional; above all, he understood the movements Brendan wanted straight away, while Stevie [Gerrard] and Jordan Henderson began a process of adapting to his style.
Recognizing the teachable moment before him, the teacher engages in a process of consultation with his students.
In fact, in 1791, one wealthy Virginian, Robert Carter, began a process of freeing 452 of his slaves.
The element of moral fervour that underpinned everything Benn did came from his nonconformist conscience, which made him view life as a process of self-improvement and his career as a duty.
