Can keep be used as a replacement for store?

One of google's definitions for keep is:

put or store in a regular place.

"the stand where her umbrella was kept"

synonyms: store, house, stow, keep a place for, put away, place, put, deposit, stack, pile "the stand where her umbrella was kept"

To me, the example and some of the synonyms don't quite work together. My question is can keep be used in place of store in this sentence: 'I stored my wallet in my pocket.' Would the sentence be correct if I wrote 'I kept the wallet in my pocket.' (The scenario is that the wallet is already out of my pocket and I'm putting it away in my pocket.)?

Using "kept" makes it sound like the wallet was already there. You'd be better off with a verb like "stored" or "put" which suggest that the wallet is in the process of being tucked away.