The extended warranty (if from BMW) definitely transfers with the car, no paperwork involved just take it to the dealership when she calls for service. I know this first hand for a fact.
2015 BMW M4— Mineral White on Sakhir Orange/Black DCT
2012 BMW S1000RR — Racing Red/Alpine White
2009 BMW M3 Coupe — Alpine White on Fox Red, DCT - Sold
2003 BMW M3 — Carbon Black on Black, 6MT - Sold
1995 BMW M3 Coupe — Cosmos Black on Black - Sold