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[jelly92784]

No: HPFGUIDX 158255

This is a really interesting question to think about.  I've noticed a 
few people talking about the way that Jo phrased the question, 
focusing on the "at the time" part.  I just wanted to point out the 
one thing we do know about the cloak, which is that Dumbledore told 
Harry, "Your Dad left it in my possession before he died and it is 
time it was returned to you" (or something along those lines, don't 
have my book for the exact quote) in the note he gave him along with 
the cloak.  This points to James voluntarily leaving the cloak with 
Dumbledore for some reason, probably not being aware of the fact that 
he was going to die soon and would never get it back.  So the question 
could be why did James give the cloak to Dumbledore, or possibly, why 
did Dumbledore ask James for the cloak?