You can have a cured and smoked ham internal temp at or above 135° and you have a 'partially cooked' ham, it must be baked to a safe 160° internal before serving.
For what is considered 'fully cooked' ham would be at or above 146° internal at the time of it's original produced weight. Through analysis, inspectors can send in samples of hams and tell exactly what temp the product reached before cooling; we had to submit samples for analysis every month minimum, picked up and sent in by (at that time) State Inspectors. We would get a printout on all the particulars and if the sample passed or failed (never had a failure!) on water content % (always was 0), temp reached, salt content, cure content, etc. etc. (Now it's done by Federal Inspectors, not State).
To legally pass as 'fully cooked' the internal must be 146° or greater original temp. But, you're instructed to always reheat the ham to 160° or greater. Why? You have a big piece of meat. If you probe your ham and somewhere near the center it is 160° or greater, you can safely figure it's at least over the 146° minimum. If you take it to 146°, it is possible that there are areas under that temp and could be dangerous.
Speaking of ham and water content, many people think that producers intentionally inject water into the meat to up it's weight. That is not true at all.
If you start out with a 20lb. fresh hind leg of pork and inject 4 lbs of brine into it, then you've increased the weight of the product 20% thru injecting and soaking. You put it in the smokehouse and after it is smoked and fully cooked and you weigh it and it's now 22 lbs, you've net increased that product's weight by 10%. It now must be sold as "10% water added ham product". I've seen ham products at 30% or greater water-added. But it's determined by comparing the original weight to the finished product weight, not any other factor.