Upvote:4
There are several aspects to the question. The Swiss consulate did the recommended thing and you can certainly use your German visa for the first part of the trip, as long as it is a multiple-entry visa and there is no gap between your two visas. We already have a few questions on this, e.g. Traveling on back-to-back Schengen visas
An additional complication in your case is that your old visa is in a cancelled passport but that's OK too. I am not able to find a reference right now but there was even a court case about this (I mentioned it in a comment to some earlier question I think). What you need is (1) a valid passport and (2) a valid visa, not a valid visa in a valid passport.