I partly agree with Eva. My great-great-uncle Abraham Lob Beer, born in Moravia in 1858 has Beer in the birth register entry, but is indexed as Bär in the register index. (I hope that the umlaut shows up).
Thus I read "Jakob bar Moscheh Bar" as Jakob son of Reb Moshe Bär"
I would also be interested in how Beer is written in the Hebrew script. My Beer ancestors use bet ayin ayin reish.