Yes, they're 100% compatible. (Craftsman sold in the US, Stanley everywhere else) : r/Tools
subtel® Battery Replacement for Stanley FMC625D2, FMC645D2,FMC675B, FMC688L, FMC675B-XE, FMC698B FMC 687L Cordless Power Tools - 18V Li Ion 5Ah: Amazon.co.uk: DIY & Tools
STANLEY FATMAX V20 18V Cordless Jigsaw (battery not included) (SFMCS600B-XJ) | Homebase
STANLEY FATMAX V20 18V Battery Adapter (SFMCB100-XJ) | Homebase
Batteries & Chargers | STANLEY
Argos Product Support for Stanley Fatmax 18V 2.0 AMP Charger (244/8574)
STANLEY FATMAX SFMCMW2651M Battery-powered Lawn Mower , best deal on AgriEuro
STANLEY® FATMAX® Power Tools Hard to Beat - 18V Battery - YouTube