In all Lithuania records at www.jewishgen.org we have found only one Bernshtam:

 BERNSHTAM Bentsion,
	 who wrote application for Feyga Merkel, 
	 from Raseiniai Court Files on Inheritance 1875
	 in Raseiniai, Kaunas gubernia.

It seems (I'm not sure) that Raseiniai, Kaunas gubernia is Zhagorsk, Kovno gubernia (Kovno = Kausans), and so this man is likely a father of Isakhar Ber Bentsionov Bernshtam from Melitopol metrical books.

Interestingly, that famous russian poet Ostap Mandelshtam wrote in his memories, that Zhagorsk was Courland town.

Bernshtam German graduated Vilna gimnasia at 1846 (from http://www.petergen.com/history/wil1gim.shtml)