Should work right away if gassed up and running.

The condensor is right at the front on these so easy to see if it is shiny and new. They are a very common replacement.

If it is full of gas then you have an additional problem. If it hasn't been working for a while it is possible the compressor has siezed due to inaction.

Firstly,the fact that the garage said it would take a while to work after the repairs,shows them to be totally incompetent .Also ,you say it stopped working overnight, tends to suggest that the condenser was not at fault.Unless somehow overnight you sustained a leak.Possible but unlikely.If this car if fitted with a GM/vauxhall derived engine,then I would think the failure could be a compressor or wiring/circuit fault.Take it to an indy a/c specialist.

It's good that you've qualified that you went in with a fault, no a/c and asked them, as experts, to fix it, instead of you going in saying, I've got no a/c, I think it's the condensor, sling one on for me please.

They've done a bad diagnosis, landed you with a hefty bill and you still have no a/c. The system should have worked straight away if the condensor was the fault and they had purged the system correctly and refilled the oil and repressurised the system properly. Junk can get into a system if it is left depressuried for a long time or an ancient, decaying component starts shedding debris into the system. That doesn't sound like the case of yours, if it was working one day and failed the next. Get your money back, they are entirely clueless.

Reminds me of the crap mobile mechanic who, "serviced" a friends car years ago and while it ws still not running very well a week later, told him that the new spark plugs would take a couple of weeks to work their way in.