Edit 2: I find the question very interesting but not well presented. As long as it doesn't become clearer, here's how I understand the issue:
The OP's friend did his PhD with his PhD advisor. At least part of his work was not eventually published as the PhD advisor considered it inadequate for publication. The PhD student finished his PhD and went to work in another group in the same subject. He added a few more data, bringing the work to what he and his new group considered at publishable level. So, they wrote the manuscript (or planned to) adding the work from the PhD, plus the extra 3 months of work from the new group and offered co-authorship to PhD advisor. The PhD advisor was not aware that his ex-student was continuing working on the same subject and had not agreed in advance on this collaboration.
The acknowledgement is a detail in the issue. The actual issue is the authorship and the "collaboration". (That's how I understand it).
Also, the contribution of the PhD advisor was zero for the post doc, but was present in the PhD period.
If things are like that, then this is my "answer" below. If not, my answer is at the bottom.
Just to clarify, I don't answer in respect to how reasonable reaction it is for the career of the ex-PhD student. I answer if it is reasonable in the context of research collaboration and supervision and try to identify where mistakes were done. It's quite obvious that this behaviour obstructs the career of the student, but there are obvious or subtle rules in research (as in every workplace) that, if not followed, can lead to problems like this. End of edit 2.
I think that his PhD supervisor has valid reasons to be angry (provided some missing information are true).
Fist of all, most of the work was done during your friend's PhD, so as part of his PhD, it seems like his supervisor has the last word of what should be published and how.
Also, I assume that the continuation of the work was not agreed nor approved by the supervisor of the PhD, thus he's angry realising that the work has been continued without his approval.
So, in a way I can feel for him. It's his project (and your friend's) and he should decide if he wants to include your lab (in the work and) in the publication and not vice versa.
Edit: In this case, your friend would have to convince his PhD advisor of the importance of the new collaboration (as he should have done the moment he started his new post). If that doesn't work, he can discuss with his PhD advisor what he thinks is needed to make the work publishable and how this could be achieved from this point on. At the same time, work with the new team and/to submit a manuscript without the PhD work involved. End of edit.
In the case that it was agreed with the PhD advisor to continue the work on a project in the new lab, and now he backs off, then it's him on the wrong side and that's something the PIs have to sort out.