I assume from your question that you own the tank. With that assumption- is the tank within it's test date? On the neck of the tank is the date of manufacture, or subsequent test dates. The original manufactured date is good for 12 years, the test date is good for 5 years. I would suggest that you take the tank to a propane supplier for repair. If in fact the tank is out of date, it may be worth your while to just purchase another tank, as the cost of the tank repair & testing may be more than a new tank- I'd price it both ways before making a decision.

No, it is not a common practice since there should be a dedicated "fill port" fitting included in the valve end of the cylinder.
But I don't know where you have been getting your tanks filled.
There would not be any harm done to the tank if a fuel vendor filled the tank through what is the delivery valve, but I can't see any reason why they would do that as it would take a bit more time to fill it through the smaller delivery port than the much larger fill port.
The tank should really be filled by weight using scales.
In lieu of weight filling, the tank should only be filled until a small shot of liquid propane escapes from the very small purge valve while the tank is oriented in the horizontal position with the tank index pin slot/hole at the 6 o'clock position (same as when the tank is in its horizontal mounted position).
These tanks must never be filled more than their specified volume by weight or above the level of the purge valve at horizontal. This is to assure adequate room for thermal expansion of fuel and pressure increase from same.

Thanks will do. Is it common practice to fill these tanks through the shut off valve?

Fisher, if the tank valve stem is leaking and you have not even connected it to the forklift, you might need to have a new valve installed in the tank.
But.......because the fuel is in liquid state at the valve area, a fuel leak that only lasts a couple of minutes (after closing the valve hand ****) or so may only be due to some wear in the valve packing and/or valve stem. If the leaking continues for more than a few minutes after closing the valve, you probably have a defective valve assembly. If the leaking stops a few minutes after closing the hand **** you may be able to tighten the packing and stop this leakage.
Look directly behind the hand wheel **** and see that there is a packing gland nut that the valve stem goes through.
After LP cylinders have been in use for a long time, the valve stem and the packing material inside the valve can develop some wear, resulting in a leak as you describe.
I suggest you try to tighten the packing nut about 1/4 turn (clockwise) at a time and recheck for a leak.
If......you are unable to stop the leak in this manner (as is the designed method) then you need to have the valve replaced.
This would require an empty (and purged) tank and is best left to a propane distributor service facility as I believe there might be some certification details to be addressed in cases of valves and such being replaced.
In the very least you would need to purge the air that will enter the tank while the valve is out before refilling the tank completely.