Weirdo guy sprouts wings is angel

This movie was mid to end 80s. Drama/suspense. Some girl lives on  an apartment and is watched by this weird guy (long hair, over sized sweater/jacket, glasses .. maybe shades) and it seems like he is fixated in her. In the end it turns out he saves her and there is this end scene where he is in an elevator and sprouts wings, and flies upw through the escape vent. Apparently he was something like her guardian angel.

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