Two friends of mine, Alice and Bob, enrolled in two different Ph.D. programs, have been collaborating in a research project and writing a paper together. They have submitted the abstract to a certain conference and hope to publish the paper in the future (the conference allows this). Alice, expecting to graduate sooner than Bob will, asked Bob by email if she could include the paper into her "staple" dissertation. Bob is completely fine with that, but he is confused at the same time, since her email was lengthy for the seemingly simple favor. He thinks that perhaps the favor would have consequences according to some customs in the academia; he is worried that the decision might make it impossible to use the paper as part of his own dissertation.
Question: Can a single co-authored paper be part of two stapled dissertations (by two people)?
(Alice is in the Netherlands, and Bob is in the U.S. They both are enrolled in interdisciplinary programs, but the closest fields include mathematics and theoretical computer science.)
Every university should have guidelines around how publications can be incorporated into a PhD thesis. The correct advice (as @Andreas notes) is to consult these guidelines. Furthermore, it seems that PhD by publication is becoming more popular and guidelines are evolving.
I'm familiar with various models of "PhD by publication". At my institution in Australia, the PhD student is expected to be first author on any major publication that forms part of a PhD by publication submission. They also need to attach a form for each publication outlining their contribution and the contribution of the other authors. The form needs to be signed by the other authors. Non-first-author publications can be included but they are intended more as supplementary contributions. Exactly what this means is a little open to interpretation.
By way of a concrete example, here is an example of such a policy (the policy at your university may differ):
It is expected that the student will be the first author on the papers, as per 1 above; the number of co-authors is limitless. Students may be second or later authors on additional papers.
Thus, to answer your specific question, at my institution, a paper could be included in more than one PhD. However, the student who is first author would have a stronger inherent case for it being seen as an integral part of their thesis. Furthermore, the contributions of all authors would have to be explained.
You may want to consider practical alternatives such as thinking about how the work could form two papers where you each drive one paper as reflected in being first-author on that paper.