That's not valid I'm afraid, once you reach a London Terminal (e.g. Waterloo East) you may continue to or through others (e.g. Charing Cross) but you may not go through any stations that are not London Terminals (e.g. Clapham Junction).
Your friend could change at East Croydon for a train to Victoria if on a train that stops there, otherwise would be best off using Oyster or a contactless payment card to get the tube (from Charing Cross the quickest way is to walk to Embankment and get the Circle or District lines)