The second sentence is incorrect. You can not “have” something before it has become.
They now have an interest in snakes because they became interested in them in the past.
2 décembre 2017
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There isn't much of a difference- but I would always use the first option, 'when did you become interested'. I don't think I've ever heard someone ask when someone else 'has become interested' in something.
2 décembre 2017
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