I see fun times in your future.
What version of Inventor?
What version of SolidWorks?
You will lose feature history tree and assembly constraints (going in either direction) and will need to run Feature Recognition in both.
Assuming not everything was done incorrectly (in either) or needs changing - I recommend only recognizing those features that need to be changed. And you can always use direct editing techniques.
To keep frustration to a minimum - treat the problems as geometry problems and do not get hung up on software. The people out on the shop floor deal with 3D geomety problems every day.
The ways of working backwards-is that like a martial arts thing?
You can export a solidworks model or assembly to Inventor through the save-as dialog. Look in the software help for the particulars of what will be lost in the translation.
You can also open SolidWorks model files in Inventor-though they have to be saved as inventor files in order to use them. Look at your Inventor documentation.
But, for the sake of your career, I advise you to do the project in Inventor if that's what they want. All you're doing by insisting on using SolidWorks is introducing unneccesary translation issues into your schedule and the argument, "I'm significantly more productive on SolidWorks than I am on Inventor," is hard to prove and usually tests the boss' patience. Besides, you're getting the chance to learn a different CAD package and you will certainly find things in Inventor that you wish were in SolidWorks and we'll all benefit from your broader experience.
Atleast frame the argument this way, "in order to do my work in Inventor, I will need some time set aside to read the documentation, do the tutorials and learn the particulars of using it." Maybe you're boss will put you in a 5-day training class.