No, for him is a prepositional phrase. A gerund is a verb form. Although it is used as a noun, the phrases that are used with it are those that are appropriate for verbs.
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What I wanted to know is the prepositional phrase that I used--for him.You wanted to know the prepositional phrase that you used? I don't understand what you mean by this. We both can see that the prepositional phrase that you used is for him.
According to the author (sorry I dont remember his name),