There is no such thing as a cross-site duplicate. As long as the question is legitimate, it should remain open where it was posted.
(Note that this doesn't apply when the same user posts the same question on multiple sites. This is generally considered a waste of people's attention, because it leads to duplicating the work of answering the question.)
I would copy-paste the answer in a citation block (with attribution, of course):
On Gaming Stack Exchange, Joshua Carmody posted an awesome answer on a similar question which I shall reproduce here:
Often the best answer in one community is not the best answer in another community, because different communities have different expectations (for example, answers on Gaming tend to focus on gameplay, whereas gameplay is off-topic here). This seems to be an exception.
Please leave a comment below the question on each site, with a link to the question on the other site. This way, someone can easily find other answers that may have been posted on the site they didn't find first.