USPTO overseas: filing and prosecution from Israel

Just over a year ago, I was entrusted with directing the US operations of JMB Davis Ben-David. As our firm is based in Israel, I was to do this from my desk in Jerusalem, some 7,000 miles away from the US. Given the way IP law is traditionally practised globally, this was not an immediately obvious service for our firm to provide. After all, how can an IP firm located outside the US represent a client before the US Patent and Trademark Office (USPTO)?