Yes.
But it is a decision I would think long and hard about. with the j1 you block yourself from immigration into the US for whatever length of your residency +3 years. So, if your objective is to stay in the US for good, consider finishing your residency, get a greencard and go back to your specialty of choice later on. if immigration into the US is lower on your list of priorities than advancement in the career of your choice, think about it for a week and go for the j1 (But not until after you have gone through the entire hierarchy at the receiving institution trying to convince them to take you on the H1b transfer. btw. with the H1b transfer you can start next week. With a J1, you have to go through the entire rigmarole with ECFMG and a change of status request. With a H1b transfer you are allowed to start working the day USCIS receives your employers application for the transfer. Something to think about for your employer).