A morning stroller (What do you call a person who strolls in the morning?) found a shoe with a leg in it.

1. Is the sentence correct?
2. What do you call a person who strolls in the morning?

I believe what you have is fine.

A pedestrian, out for his moring walk/stroll.

A morning jogger would be called a morning jogger, or perhaps an early morning jogger, or runner.
1. Yes
2. You have espressed it accurately.
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Thanks, Philip and Avangi.

It was a shoe with a foot in it.

Clive, good catch. Actually I purposely used leg to see if it is acceptable and wanted to see how native speakers would respond to it. You are the only one who's pointed it out. Let's say there's a leg with a shoe on it, should I say foot or leg?

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I think that if you found a human body part during your morning stroll, that would be what you (and everyone else) would focus on, rather than what the bit was wearing.

I found a foot. It still had a shoe on!

I found a leg. (blimey! who cares about the shoe.)

You wouldn't say 'found a sleeve with an arm in it' or 'found a hat with a head under