How to  Assign multi-select records for Selected user and Allow Permission to view by only the User.

I have couple of users (user-A, User-B, etc.) and couple records (record-1, record-2, record-3, record-4, record-5, etc.)  in the application. 

I want to create one form with multi-select for records and lookup for user. on submit Select records must assign to the selected user. 

Such as for user-A assigned records  record-1, record-2, record-3 and  user-B  assigned records  record-4, record-5

Once done the selected user only have to view the records but any other users.

Please advise URGENTLY.

Thanks.