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.
2012 BMW S1000RR — Racing Red/Alpine White
2009 BMW M3 Coupe — Alpine White on Fox Red, DCT - ESS | Turner Test Pipes | Macht Schnell Stg 2 | OEM Performance Splitters, Spoiler & Mirror Caps | 3D Design Diffuser
2003 BMW M3 — Carbon Black on Black, 6MT - DPE | B&G | K&N | JL AUDIO - Sold
1995 BMW M3 Coupe — Cosmos Black on Black - Sold