Unfortunately I don't think the replies that "single mothers get priority" are actually accurate. At least, for daycare and
kindergarten spots, single parents and families where both parents work are the same level of priority. And anyone who wants a spot in a Hort is going to be one or the other of those classifications. Also, I think for September Hort spots your girlfriend probably already missed the sign-up cut-off, as I think its the same as for Kindergarten, at least the Kiga form I filled out also included information for Horts. That said, good luck, and here's a
link to information on public Horts in Munich.
Also, FYI some schools offer something called "nachmittagsbetreuung" -- this means the kids get to stay longer but they don't get help with their homework like they do at the Hort. Switching to a school that offers this option is viewed as a valid reason for a Gastschuleantrag to be accepted from what I've been told--I don't know how competitive it is to get into these spots.
Edit--here's
another page on the munich website with more links to Elterniniative, Nachmittagsbetreuung etc.- all the options for Grades 1-4.
another edit--sorry, probably if your gf just got a rejection from the Hort where she signed up then she did so by the deadline...but maybe Nachmittagsbetreuung is still an option...