Thanks for the offer. Here's some files on technology we've adapted. Given what you've said about your situation, the capacitor and power tech is most likely to be useful, maybe also the construction. The force field technology and FTL engines, we're still working on and not quite ready to share (though the FTL isn't useful without the dust-cleared space lanes anyway).
Adjacent to medical technology, if you have any designs for advanced chemical analysis, that would be massive. We have a really useful chemical, Cruezzir-D, which can heal basically any nonlethal injury quickly and can produce supersoldiers (with some, manageable, psychological drawbacks) but it falls apart under analysis, just water and some complex organic molecules. Anything you could give us that might help us reproduce it ourselves would be a huge force multiplier.