You can turn on 'font substitution' but that lends itself to an entirely new set of problems, a major one being having to do typesetting everything from scratch again. For the long term problem, there's no solution really. Any artwork you receive from a designer should be packaged with the fonts they used so for your immediate problem it may be best to let the designer know you need the fonts. I understand completely, it's a constant problem. It's not about being an 'authentic' file or having the original font bought from its founder, it's about avoiding a 'missing fonts' notice.
