Overlapping post-doc positions I have a 3 year post-doc position at University A and also have been offered a 3 month post-doc position at Research Institute B. To be precise, the invitation letter from B is worded as follows:


  We would like to invite you to spend three months at Research Institute B. For your research work in collaboration with the mathematical community at our Institute, we will offer you a monthly research grant in the amount of XXXX. By accepting this grant you do not become an employee of Institute B.


The position has a flexible time so I can go for any continuous period I like. I would like to accept the invitation and go during the summer so that it doesn't conflict with my teaching duties at A. However there will be a period of about one month of overlap. My idea is to commute during this month, as I only have to teach one day a week at A, and no teaching at B; and it's about a 5 hour train ride. So I could spend about 3 days out of 5 at B and the other two at A, for the period of overlap.

My question is: is it ethical for me to do this? Would I get in trouble with University A or Institute B, if either found out?

I have heard of someone doing something similar, but I don't know the details of how that worked, so I want to be sure that I wouldn't get into trouble for this.
As a department chair at a US university who has on various occasions negotiated these sorts of overlapping/adjacent postdoc arrangements with job candidates, I can tell you that at least in the US (and, I strongly suspect, in many other countries) it would be considered highly unethical to set up an arrangement of this sort without informing and getting the agreement of the directors/department chairs at both institutions A and B, and is very likely to get you into trouble if you are found out (an event which itself seems quite likely, although that is harder to estimate), with possibly very bad consequences for your career. You can be sure that the negative financial effects of those consequences (even assuming money is the only thing you care about, which probably is untrue) would be of a much greater order of magnitude than the extra money you are trying to squeeze out of your third month of stay at Institution B. And keep in mind that this is not just an ethical matter -- at my institution specifically you would certainly be violating some institutional policies, even if in a practical sense you would still manage to meet your teaching obligations. If you are somehow thinking that "it is better to beg for forgiveness than to ask for permission", please trust me -- this is not a situation where that saying applies.

In short, DON'T DO IT. Bring the department chairs and/or faculty mentors on board and see how they can help you achieve your goals. As I said, in my department we occasionally try to help postdocs combine their stay at my university with another short-term visit to another institution, and recognize that this can work to everyone's benefit, but it must be done honestly and with the full knowledge and cooperation of all involved parties.