Duh, this is an important and somewhat "delicate" issue, you have hit a nail on the head ... ;-)
There is no official policy about it (I am personally not even sure if there should be one?), I can only put down my own thoughts about it and hope other people will do the same in additional answers. I personally would leave it open to each member of PhysicsOverflow, if he likes to leave for example a comment summarizing his answer (or the answer of somebody else) at the site where the question is imported from.
The question "to leave or not to leave" a link to an answers here, is by no means spherical or isotropic ;-), as different points of view (or directions different people might look at it) have to be considered:
- The asker of the question on the other site is probably interested in learning about the fact that he has obtained an answer and could be happy about it.
- The answerer may obtain well deserved additional love and attention for his post.
- For PhysicsOverflow it is a nice means to naturally make the site more well known among the targetted and potentially interested audience.
- Concerning the (official) take on such comments of the site the question is imported from, it should in principle make no difference if somebody leaves a summarising hint or comment giving a link to further information on Quora / PhysicsForums / a blog post / a paper / a news article / Math SE / MathOverflow/ or PhysicsOverflow / etc, as PhysicsOverflow does not have any reservations against such comments linking to other places in the internet either, as long as the information provided is related to the question, on topic, and useful for the community. However, different sites we import questions from may adopt slightly different (more or less official) attitudes in particular towards PhysicsOverflow (the answer in the second link has +9/-8 votes at present).
In addition, some people can be contacted privately, which has the only drawback that other people reading the question would not learn about the answer ...
Taking all these things into account, I personally would leave it open to the members of PhysicsOverflow to decide if and how they want to contact the OP of an imported questions.
Other thoughts ...?