On Saturday the Pink and Blues travelled to Sussex in the first qualifying round of the competition and they defeated their Bognor Regis based opponents 3-0.
A brace of goals from in form striker Gavin Tomlin either side of a Mark Weatherstone effort saw the Champion Hill side progress against opposition who play two levels below Hamlet on the non-league ladder.
On Monday Dulwich were drawn against Hendon in the next round of the tournament, a home fixture taking place on Saturday September 17.
Hamlet and Hendon both play in the Ryman Premier Division and only came up against each other last week when the pair played out a 1-1 draw on Bank Holiday Monday.
Should Dulwich overcome their north London opposition on Saturday week they will pick up £4,500 in prize money, having already pocketed £3,000 for the win against Pagham.
The Pink and Blues are back in league action this weekend, at Champion Hill, when Burgess Hill Town make the trip to Southwark for a 3pm kick off.
They follow this up with another game on Tuesday evening when they play an Alan Turvey Trophy contest against Grays Athletic, a contest that commences at 7.45pm.