I'm told that it should not take much more than a week.

I'm a recruitment Manager & I sometimes talk to people who have waited several months. This is always the fault of the company. After 1 month, I think that you should discuss with your company & insist on a follow up.

You are effectively in "limbo" at the mercy of the company - so maybe it's just inefficiency on the part of your company, but maybe not.

I'd check & then check again.

It's the squeeky wheel that gets the oil!