I am currently applying for masters in CS. My undergraduate main project, which was later made into an IEEE publication, was done under the guidance of an assistant professor, who is currently pursuing her PhD abroad. Being a student at present, she would be unable to obtain a letterhead from her university. With what degree of credibility would such a recommendation without a letterhead be viewed by admissions committees? Also, will the current credentials of my recommender (PhD student) cause the LOR to be reduced in value? My target universities are in the US, Canada and Europe.
I am the Graduate Coordinator for my department (mathematics at the University of Georgia).
In general I absolutely do not care about the letterhead of recommendation letters. In fact, the electronic system at my institution gives writers the option to fill a(n unlimited in size) box with text, so a lot of our recommendation text does not come in letter format. Moreover, when I write letters for students, I usually do not trouble to use the university letterhead (having observed hundreds of others doing the same practice).
However, your current writer was an assistant professor and is now a PhD student. In my experience that is quite irregular, unless the recommender already had a PhD and is now pursuing a PhD in a different academic field. The status of the letter writer does play a role in how we evaluate the letter, and I think many faculty would devalue a letter for a graduate student that comes from another graduate student.
So I think this is case in which official letterhead would be helpful, if it can be honorably procured and used. Getting a letter from a former faculty member is not really any worse than getting a letter from a current faculty member -- after all, in many cases they are writing about a former student. If the letter writer was legitimately an assistant professor at the time they worked with you, then of course they can say that. They should also mention that they are not currently faculty at that institution and provide a means of being contacted (email should be fine). I am not completely confident about it, but at the moment it seems to me that the writer does not need to say that they are now a PhD student elsewhere -- it is not directly relevant to the evaluation and may cause the letter to be devalued in a way that is not necessarily fair to the student.
Another possibility is to get the requisite number of letters from "real faculty" and include this letter as an "extra one." If that is not technically possible with respect to the admissions system, you could arrange for this person to send the letter to the chair of the admissions committee, or you could ask for her to write a letter jointly with a "real faculty member" at your institution.
In the days of email, etc. perhaps she can arrange for the letter to be printed at the original place and mailed from there.
On the other hand, I think that is shouldn't make much difference if she explains that she is no longer with the former university. It could even be sent on her local letterhead with an explanation.
The reviewers want to know a couple of things. Was she a legitimate entity in your background? Is the letter truly from her and not a forgery. That is not impossible to fulfill.
On the other hand, just being on university letterhead is no guarantee in itself that the letter isn't forged.
As to her current position, if she was an Assistant Professor when your guide, her letter should be evaluated in that light, not her later associations. I can't guarantee that, of course, but you could certainly point it out to the committee if questions are ever raised.
Perhaps her name appears in your publication, also, along with some indication of her position then.
Finally, though retired, I can still get letterhead stationery from my last university. The reason for it hasn't ever been questioned, but it is easy to answer for. She could write to the department secretary.
Of course, if the receiving school specifies 'on department letterhead' then you should seek an exemption first, giving the explanation for the need.