How long is the training to get a Boeing 777 rating if one has a 737-200 rating?
A flight school can offer an "abbreviated type rating course" which takes into account skills from previous type ratings, assuming you have flown an adequate number of flight hours on those ratings.

Boeing also offers a shortened type rating course, details are halfway down their page. To answer your question, Boeing claims 13-15 days for their training and requires 1,000 hours of experience, but it does not depend on a specific rating. There is an even shorter 777-787 conversion as well, that requires a 777 rating.

I think their assumption is that they can skip a lot of basic handling, CRM, checklist type training and focus on the technical aspects. A training provider with the proper approvals could offer a similar class.

Also, for reference, there is the Airbus A320-A330-A340-A380 conversion training which uses the proprietary term "cross crew qualification", and takes less than 2 weeks versus 6 for a full rating. This is done under a EASA approved syllabus, which allows you to do it at any qualified school. Here the requirements are 150 FH on the appropriate Airbus type, and 3 months of experience.