According to the following extract from M-W Learner's Dictionary, you should follow the style that is preferred by your employer, since there is no strict rule. It may either be Fritz’ friend or Fritz’s friend.

  • There is a lot of disagreement about the answer to this question. To form the possessive of a proper noun ending in an s or z sound, some people use apostrophe + s, as in Perez’s and Burns’s, and others prefer an apostrophe alone, as in Perez’ and Burns’s [sic].

  • The best advice I can give you is that if you are writing for a class, or if you work for a company or other institution, find out which style your teacher or manager prefers and use it. Otherwise, decide which style you like best and use it. However, be consistent – don’t use both styles in the same report, letter, memo, essay, or whatever you are writing.

  • One more thing: Since my name ends in –s (Mairs), I think about this question a lot. For a long time I thought there was only one correct answer, but I have since learned that that’s not true.

In the 2010 edition of the Chicago Manual of Style, the editors reversed course.

  • Now Chicago calls for always adding the apostrophe + "s" regardless of spelling or pronunciation.