Yes you can provided its not on the fast boost setting, a nice steady 2amp for a few hours is best until its fully charged and you dont need to disconnect anything or remove the battery.
Put the red lead on the + terminal of the battery first then the black earth lead on the engine lifting eye at the end of the cam cover, then switch it on and leave it to charge up, overnight is best.
Mind you if your battery is old it might need renewing anyway as the alternator should keep the battery fully charged, unless you do lots of very short journeys with lights on etc.
Still an extra charge wont do any harm.
If trickle-charging it overnight doesn't bring the stop/start back, it's probably not a battery problem.
Don't be surprised if charging up the battery makes the stop/start work but after a few days it goes back to its old ways - that does indicate the battery is 'tired' but by no means at the end of its working life. And it's not worth replacing the battery two years or more before you have to, just to get the stop/start to work.
I had a hire fiesta with stop start and don't like it, better than on the Chrysler Ypsilon that was very dim witted. I'd turn it off for a bit, I can't help but think I know it's for the environment but you probably save less in petrol than costs of batteries or alternators problems
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