You can go to Westley Richards home page and enter the serial number of the gun in the "Member's Room" section of the site and find out the age of the gun. To get any historical records will likely cost a fee for Westley Richards to give you all the information they have about the gun.
http://www.westleyrichards.com/It appears to be a standard Anson & Deeley boxlock (the locks fixed with the pins visable on the sides of the receiver, Westley Richards is famous for their detachable lock guns ) and a camming top lever. The stock cut down is a shame, but has happened to other guns as well from a split butt or an owner looking for more length of pull. If taken proper care of, it should be a decent gun. If you want to use it and don't know much about the gun then have the gun checked out by a gunsmith who really knows side by sides, or have Westley Richards check it for you. No one will know their guns better.