I recently saw a story where a City Weekly filed a FOIA request and received a trove of emails in response. Is the receiver required to publish a link to the source? Is there a way to get access to the files / emails without resubmitting a request?
Short answer: No. As other people have said, the recipient of the FOIA information is not obligated to share it with others. There are some FOIA allowances for the needs and benefits of providing information to media, primarily with regards to fee waivers, but the recipient can do whatever they like with the information once they have it... including keeping it all to themselves.
That said, there are various initiatives to try to make these requests more useful by sharing them with a larger audience once they have been made. On the Federal side the most prominent that I am aware of is FOIA Online, which serves both as a conduit for requests and a place where others can see the responses. Unfortunately the participation seems to be voluntary and not all agencies participate.
On the public side you have projects like Muckrock which has submitted requests and responses listed and possibly FOIA Machine, which was kickstartered into existence earlier this year by the Center for Investigative Reporting. I'm unsure of FM will make public responses to other people; I can imagine a case for journalists to not necessarily make other journos aware of what they're working on.
In voluntary participation people often put results into Scribd or DocumentCloud and that might be your best avenue here - contact the people who made the request and ask them to put the results into there and share them. Here in the DC area people at the City Paper put supporting documents in one of those and attach them to the bottom of their online story. Your best bet may be to convince those folks that doing so would enhance their reporting.
This depends on which city you are in too- as of last year in Oakland if you did ask for the exact same request, it may not have helped you much as the process was so poorly setup they couldn't always benefit from repeat efficiencies.
But now we have an online request system that published all requested info by default- except certain crime info which is only available to the victims directly. This means all requests will be visible, you can just find past requests often and don't need to repeat the ask- incredible option all cities need to adopt.
The receiver does not have to republish. If you make a new request, you may get a response very quickly since the original agency already responded to the City Weekly request.