Yes, it fits. The Patona homepage states:
The battery is suitable for the following models:
Dyson
V6 Hepa, V6 Absolute, V6 Fluffy, V6 Pet, V6 Pet Pro, V6 Car & Boat, V6 Baby & Child, V6 Top Dog, V6 Motorhead, V6 Cord-free, V6t Mattress, V6 TriggerDC56 Handheld, DC58, DC59, DC61, DC62, Tier, DC 62 Tier Pro, DC72, DC74Tier, SV03, SV04, SV05, SV06, SV07, SV08, SV09, HH08