Can I copy a report from one app to another

No.

I believe you could--if the apps are truly identical, meaning the field IDs are all the same--copy the expanded URL from the report in one app, e.g.:

?a=q&qt=tab&dvqid=17&query=({'4'.XTV.'-56303012'}AND{'1'.IR.'last+1+wk'})&clist=35.72.57.58.74.56.36.3&opts=nos.

and paste it into the other app, then save the report.

I have not tried it, but I don't see why it would not work

Yes. Good thought. I suppose if you had a complex set of filters that you wanted to avoid redoing, that could work.

Everything is possible. I do this all the time using the TamperData FireFox plugin:

https://addons.mozilla.org/en-us/firefox/addon/tamper-data/

How do I find the expanded URL?

Thanks for this. I just did it with a very large set of filters and it worked like a charm.

Better still, I moved the logic for the filters into a formula checkbox in the relevant table, and now I just filter on that for every report.

No problem.
Go to the target table where you want to build the new report and run a list all report.
The URL will have a ? in it.

Paste the expanded URL starting at the ? and leave the stuff before that.