How long does it take to receive funds once an executor is appointed?

There is no easy answer; the answer, unfortunately, is "it depends." First, to state the obvious: it is possible that the conservator is doing something inappropriate, or previously had done something inappropriate, with the funds (e.g. invested them poorly, taken some for own use, etc.) and the funds you think are there are not and he is hiding that. I am not suggesting that is the case, or even is likely, but it is *a* possibility and I mention it because at some point, if you become convinced that there is no legitimate reason for the delay, your recourse would be for the executor (your mother) to bring a lawsuit on behalf of the estate against the conservator to get the money.
However, there are certainly legitimate reasons for a delay, such as:
1) When did you mother provide documentation showing her appointment to the conversator? It's not enough that she was appointed; the conversator (or anyone dealing with an estate) can and should insist on getting a copy of the court paperwork appointing or ratifying the executor before releasing money or information to them. So if there was a delay in getting that paper to the conservator, that could account for the delay.
2) When was a formal request for the funds made? Even after the conservator knows you mother was appointed executor, she needs to submit a written request for the funds.
3) If the conservator is someone who manages funds or accounts for many people (or is generally a lawyer or accountant, etc. with many clients), this may simply be working its way through his "to do" pile--it's of critical importance to your family, but may be only one of many accounts or clients to him, and so not necessarily high on his priority list.
4) It may take time to extract the funds from whatever kinds of investments they were in (e.g. liquidate assets) if they were not in "cash" form.
5) Vacation or illness or family emergency--has the person (the conversator) handling these accounts been out of the office during all or part of this period?
Other legitimate causes for delay are possible, too. But again: when you have exhausted how long legitimate delays may take, at that point, the executor may need to consider legal action to find out where the funds are and get them released.