How come you lost the fob in the 1st place? When I had keyless the fob remained in the zipped trouser picket on my textile suit and I had a cheap spare to unlock the seat, satnav and luggage on a keyring with my house and garage keys from this chap so I couldn't lose the fob. As you've found out once started the bike will carry on running even if the fob goes out of range.
keys cut to code - Replacment Keys Cut To Code - lockers, filing cabinets, roof boxes
https://share.google/iT4dHzaB6ak21Ba4I