Technically, there is no "conversion" of an H-1B from one employer to another. However, your potential employer can file a new H-1B petition for you. With premium processing (fast track), the new petition can be approved with 15 days of filing the petition. I am assuming you are in India now. If so, once the petition is approved, you can apply for a new visa at the embassy (this is the safest course to ensure admission into the U.S.). Of course, your new employer should engage an attorney to start and guide you through this process.