https://www.minimania.com/part/88G224/Classic-Mini-Magic-Wand--Remote-Gearbox-Male-Knuckle-Gear-Change
This is the male end and fits into the female end 88G223 on the back of the gearbox.If you have trouble getting the car into gear it could well be that one of these knuckles or both have worn,

My question on this male/female knuckle is "was there a zerk fitting (grease nipple) and does it have a spring and cup internal on the female part?"

It took me a couple of days but I did give him a call to chat about the problem. Seem he has moved on to a honey do project and will be dealing with the mini when he gets a chance. Nice guy with not much mini back ground. I made a couple of suggestions and ask he check back with me either way. Steve (CTR) 

Dave any updates?

Have a friend here in B.C. whose early box has just behaved the same way...box was installed assuming whoever last touched it did things properly.  An experienced Mini mechanic working in a shop owned by another experienced Mini mechanic & turbo Mini Ice Racer is trying to sort out...power unit is in the Mini.

As Alex says, the joint splines can be off by 2 splines  - in either direction. They can be removed and repositioned in the car - easier if you have smallish hands and very flexible wrists, which I wasn't blessed with (it still hurts to think about it). When they are away off, you may notice that the "H" shifter pattern may be distorted, for example the shift into first may be very long and go off on an angle. Cobradave66 says it is back-breaking work, so it sounds like he's doing it from under the car.

What makes me wonder is that the original post says "Everything was fine until suddenly while driving, I could not shift into 1st or 3rd gear.(2nd and 4th OK)", which suggests something might have failed or come apart. Hopefully it is just the ball/socket joint coming apart and reconnecting for the 3rd/4th.

"There is a little free play in the bushing from the remote ..."
In trying to follow is this bushing the 2A3502 ?  These bushings (two of them) are on the differential cover (22A249). ie. The back part of the transmission case.
The first thing I would check is with the "ball" half only (88G224) on the shaft and bolted in place can you locate all of the gears?
To reword this - eliminating the "remote shifter" from the picture can you locate all of the gears?  
As Steve asked what was done to the transmission and by whom.
Additional questions I would have - have any parts been changed in the remote shifter, was a new remote shifter mount installed.

I have been doing mostly rod change trannys for 15 to 18 years now. I still do magic wand and remotes and they are a pain compared to rods. You mention you restored your 67 Cooper S. What was done to your tranny and who did the work? You mention it was fine then it was not. You also state you can move the ball and socket and get different gears just not all. My contact info is in my profile and I'm a bit north of you Hampton/Newport News Va. Shoot me a email with Ph.# and we can chat. Steve (CTR)

You can indeed get the splines out of line by one or two, and that can be enough to prevent clean gear engagement.

The good news is that it isn't the dreaded upside-down selector bolt coming undone on the shaft as that would disable 1/2 or 3/4 instead of 1/3 or 2/4.

Hindsight is a marvelous thing, I always mark the positions of the selectors with a chisel before disassembling them.

I have a 67 morris cooper s which I recently finished restoring.  Everything was fine until suddenly while driving, I could not shift into 1st or 3rd gear.(2nd and 4th OK)  I can shift the linkage(ball and socket) on the splines and get 1st and third but then I could not get 2nd and 4th.  I have tried numerous combinations without sucess.  There is a little free play in the bushing from the remote but every where else seems tight.  I initially thought the pinch bolts would only pass through when the levers were in the correct position...is this correct?  seems I can shift the levers one spline and still get the bolt through.  This is back breaking work and I am about to lose it..extremely frustrating.  Please, can someone give me some advice.  This is my first mini.  Thought I could figure this out.