Re-map DB Users/Logins after Restore WITH STANDBY
Your users from db on server A will be moved to the database on server B with the backup. Then all you need is to recreate the logins with the same sid. You do this using WITH SID option:

CREATE LOGIN My_login WITH SID = 0x14585E90117152449347750164BA00A7


the sid obviously is your user sid that you can find in sys.database_principals:

select name, sid
from sys.database_principals
where type_desc = 'SQL_USER';