I am interested in applying for an open PhD position in astrophysics in Germany this fall. The thing is, I actually already worked with the group that is advertising the position. This past summer, I worked with the group for 3 months as a summer research student, so we know each other well and it was a very positive experience for everyone.

My advisor there told me on my last week that because of a new grant she received, they could take on a new PhD student. Thus, she invited me to apply formally to the PhD program her group is affiliated with, because as she said it is easier to take care of bureaucratic and organizational things. Could I ask her to write a letter for the application or would it be a conflict of interest?