Can be anything from 2 weeks to 3 months.
I think it's easy to forget this is a balancing act for decision makers. In an ideal world we'd all want decision asap but if the consequence of that is that things get rushed or weighed up incorrectly then who would want that!
That's not to say that taking longer automatically produces better decisions as plainly it does not. However, there is considerable pressure to make a certain number of decisions per day and the conversion process is being quietly slowed (possibly to a halt from time to time) because inviting someone to make a claim to PIP needs a DM to make a decision and there aren't necessarily enough to go round.
I think 3 months or above is too long but anything under that is arguable as reasonable depending on the facts of the case. Claimants tend to split into those things who think their case is open and shut and those who think their impairments are complex to the point of incomprehensibility. Both are very rarely true.