He does not need a new passport/picture just because he changed his facial hair. I'm in the same boat as your spouse and am now traveling Europe and Israel without any hiccups.
No. The passport is valid for as long as it is. The picture is embedded, can't be changed. Think about the millions of people who change their hair color, length, get botox, and that includes men's beards, moustaches, goatees.
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