It doesn't take long at all after the approval, it's getting the approval that takes so much time. The system needs revamping, it's a bit ridiculous. My friend had to hire a lawyer to get the approval pushed through after 3 denials of doing the paperwork himself. If you've already gotten the go ahead, it should only be a week or two to recieve funds.
After applying for social security benefits for daughter due to death of a parent how long does it take to receive benefits?
You should check out the Social Security Web site for up-to-date information. However based on personal experience, as long as all the proper documentation is completed correctly and submitted usually two months.