The phrase "after the process of" is correct and usable in written English.
It can be used to indicate a sequence of events, specifically to describe what happens following a particular process.
Example: "After the process of elimination, we were left with only one viable candidate for the position."
Alternatives: "following the procedure of" or "subsequent to the process of".
Questions, and the theories they sprouted, were to be deftly constructed after the process of looking.
He said he would resign, but only after the process of leadership election is settled.
The concentrations of PFOA in liquid media reduced after the process of bacteria culturing.
The Irredentists aimed especially at gaining several Italian-inhabited areas still controlled by Austria after the process of Italian unification (1860 70).
After the process of growing the penicillin-producing organisms was developed, pharmaceutical firms were recruited to further develop and market the drug for clinical use.
RCA differ from fresh aggregates due to the cement paste attached to the surface of the original natural aggregates after the process of recycling.
This paper is a study of corrosion attack types due to negligence during and after the process of welding of the system.
Fifty years after the process of dividing community lands began, it became evident that these traditional pastoral lands would turn into housing estates and farms if something didn't hold them together.
Many years after the process of authoritarian breakdown, consolidated democracies revisit the past either symbolically, to overcome historical legacies, or sometimes to punish the elites associated with previous authoritarian regimes.
Serendipity is a description applied to an innovation post-hoc, after the process of bumping into something unexpectedly turns into a new idea, a medical discovery, a new recipe, a new relationship or a new artistic movement.
Moves by the gas company Cuadrilla to exploit the unconventional gas in Lancashire were put on hold 18 months ago after the process of "fracking", which uses high-pressure liquid to split rock and extract gas, caused two small earthquakes.
