I have published a few months ago a paper for an IEEE Conference, the paper got published and it is indexed in the IEEEXplore. I have received an email from a research coordinator at the university that I am currently working on, asking for the online printed version of it. In the affiliation of the article was written the name of this institution, but I wonder if they are going to put in to be available online for free at the university webpage. In that case, that would not cause a problem with the publishing rights of IEEE?
Whether your institution plans to put it online is a question you have to ask them.
Whether they are allowed to put it online depends on the policies of the journal where it was published. You will need to read the copyright transfer agreement that you accepted when the paper was published.
IEEE policy explicitly allows the author, their institution, or other pre-print repository such as arXiv to distribute the final preprint version of any document, but not the version from IEEE Xplore. Scientifically, there is no reason to differentiate between the two, so as long as you send the final preprint version, it accomplishes the task of spreading information and there is no conflict with IEEE policy.
Many universities now have an open-access policy that reserves a prior non-exclusive license to distribute any research done at their institution. It is likely that your university has such a policy, and that is the reason for the request. You should check with your university (or look at this list).
If such a policy is involved, the natural legal question is then
What happens if an author at such a university then signs an agreement transferring copyright to the publisher?
This has been considered in great detail by Eric Priest in a study published in the Northwestern Journal of Technology and Intellectual Property, Vol. 10, p. 377, 2012. This seems to be the most authoritative work available on the matter. His conclusion is that the non-exclusive license granted by Harvard-style open access policies will remain in effect in such cases, at least under US law. This is based on a careful analysis of section 205(e) of the US Copyright Act, which reads:
(e) Priority Between Conflicting Transfer of Ownership and Nonexclusive License.— A nonexclusive license, whether recorded or not, prevails over a conflicting transfer of copyright ownership if the license is evidenced by a written instrument signed by the owner of the rights licensed or such owner’s duly authorized agent, and if— (1) the license was taken before execution of the transfer; or (2) the license was taken in good faith before recordation of the transfer and without notice of it.