Incorrect. Catholics do no believe dead people become angles. No doubt you got that idea from a Protestant screenwriter. Capra resented his Catholic upbringing and was therefore, by definition, a Protestant.
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A vast amount of catholic art portrays men becoming angels, and portrays Peter standing at a gate with wings.
There is also a considerable amount that portrays female angels, which the word of God denies, and human looking angels in ‘heaven.’