Hi
for this scenario please use linked server concept
EXECUTE THIS in server A
STEP1:
exec sp_addlinkedserver 'name of server B', 'SQL SERVER'
STEP2:
EXEC sp_addlinkedsrvlogin
@rmtsrvname = 'name of server B',
@useself = 'False',
@locallogin = 'domainname\loginname',
@rmtuser = 'login name of server B',
@rmtpassword = 'Password of server B'
STEP3:
when u access objects of server B in server A
then access like this
sreverB.tablename.columnname