My question is, is it allowed to give a wine bottle as a gift to a Christian/ non Muslim colleague at work place ?
How about if someone else buys the wine and gives as a gift to the coworker on behalf of me, would it be permissible then? And I give the coworker who bought wine, another gift evaluating to amount he initially spent on the wine bottle?

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Any interaction or delivery or passing on alcohol to anyone is not permissible and haram. This is irrespective if the recipient is Muslim or not.