OP boost (or charge battery) and start the car. While it's running check voltage at the battery OR just disconnect the -ve terminal while it's running... if the car dies then the alternator isn't charging. I have no idea why you're on this FSR kick and seem convinced it's at fault. Is there something you're not telling us and you messed around with the FSR/related circuitry in the past and are now having problems? Otherwise drop it as your "most likely suspect" unless you can show reason to believe it is. So far you haven't done that.
Here I go again doling out free advise which others will use to their benefit thus dropping my earnings more... it's the curse of being a considerate good person I guess... maybe I should stop posting on this site and become a leech on everyone elses intellectual property and only use it for my benefit. Damn those idiot techs.