The Rams are the sole Northern Premier League representative left in the competition, and host their National League opponents tomorrow night (Tuesday), after the initial fixture was frozen off on Saturday.
Their prize for winning through to the last eight will be a home game against Carshalton or Barnet, who drew 3-3 in their first tie on Saturday.
FA Trophy quarter final draw:
Brackley Town v Leyton Orient
Ramsbottom United/AFC Fylde v Carshalton Athletic/Barnet
Stockport County v Salford City/Maidstone United
Hemel Hempstead/Solihull Moors v Spennymoor Town/AFC Telford United
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