Rusty,
It depends on all sorts of things like weather and time of year. If you finish in mid-summer with some good weather, it could take 5-6 weeks. I finished my PPL(A) in September, they had a back-log, and it took about a month. My PPL(H), in June, took a little less. In the winter it can be quicker. But sometimes delays are inexplicable, and sometimes quick issue is equally so. It's a lottery, like many other things in aviation. You either learn patience or camp out at the Belgrano.
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Whirly
To fly is human, to hover, divine.