What you need to do is to tax it at your local DVLA office, not the post office. Fill in the V5 notifying change of keeper and taxation class to PLG and give them that at the same time you're taxing the car. Tell them what you're doing, i.e changing from disabled to PLG and taxing it. They'll do the lot at once in the right order.
You can do it yourself as above, but then you would have to pay for a new private tax disc as the disabled one will be sent back because the car no longer qualifies for exemption.
Or you can let the new owner complete the changes, he will have to do this immediately instead of letting it expire.. or he could be prosecuted, as he will not be entitled to the exemption, the new owner will have to pay for the new private disc if they complete the changes. !