The phrase "I entrust him with" is correct and can be used in a written context.
Example: I entrust him with the task of organizing the charity event.
Cline, Ruthazer recalls, entrusted him with some special opportunities.
Dante entrusts him with Yamato before departing.
I have entrusted him and Corky with my life, literally. .
"I entrusted them with what is effectively my diary.
I kept saying: 'Who can I entrust this team with?
I just hope that someday, the medical professionals I entrust with my treatment, or nontreatment, will pay heed.
"I would entrust my kids with him, and they are the most important parts of my life," he told the judge.
After what happened, I would entrust squirrels with Enron.
Does it matter, for example, that the word entrust is entrusted with a quote from L. Bruce — "I was entrusted with the unromantic job of weeding" — even if the L. in question is Lenny?
"Brandon Darby is somebody I had entrusted with my life in New Orleans, and now I feel endangered by him".
"If I'm entrusted with the presidency, that's going to be my top priority".
