I'm not sure whether you want a translation of "Betroffenenbewegung" or of the sentence you posted, which doesn't actually contain the term. I would translate the sentence as "The recovery movement [or Recovery Movement if it's a proper name] was set up by people who had themselves been affected by [or had themselves had experience of] xxx - where x is presumably something like alcoholism.

For Betroffenenbewegung a term like "self-help group" may be appropriate, but without more context it is hard to tell whether that would fit. There is also the concept of a "user-led" organisation, but again we would need more information to know whether that would be right here.

I would leave out "-Bewegung' in the English translation and have the sentence read "The recovery program was begun by victims/co-dependents (whichever of the latter seems most appropriate to you in context).

The recovery movement was founded by concerned parties.