I'm writing this post to avoid others the problems that have happened to me in these hours ...
Today while I was testing an electronic circuit with PIC18F2620 powered at 5V, the error "VPP voltage error 10.87V" always came out during programming.
I tried everything, I checked the connections, the voltages, without leaving. I realized only after hours, that the value of the pull-up resistor on the MCLR pin had a wrong value. Instead of the usual 10K, 2K2 was inserted, with consequent unbalancing of the voltage during the programming phase. Once the value is correct, everything has started to work normally. Be careful!
Have a nice day!