I highly recommend you QT the convict first, then make sure it has regained its strength and eating very well whatever food you feed the 150. Then put the convict in a specimen container close to where you feed the other tang to see if there is any aggression from either one. If not then leave it in there for a couple of days for the tang to get used to the new one. There still may be some posturing or sparring but that is natural with tangs at first. As long as it's not continuous and damaged fins. If there is you can also use the mirror trick so that they are too occupied with their reflection for a few days. Convicts can get very aggressive so just keep an eye out.
I just did this method adding an Asfur angelfish and yellow belly blue tang to one of mine that has a sohol, lineatus, purple and powder blue. First the Asfur, then the blue. Had the blue in the container for over a week.