Could the lab power supply have supplied significantly more than 8.5 Volts. For example a brief switch on transient?
Let me tell the story in another way. The battery of the multimeter had finished charging, and while the battery was connected to the device, I connected the power supply to the battery, so that the battery could be charged while using the multimeter. After a few hours, I removed the battery from the multimeter to test the charge level, and the device only stayed connected to the power supply , and while testing the battery, I noticed the wrong measurement, and from then on, it stopped working properly.
My power supply is accurate,on the other hand there is a power regulator ic on DMM board.
What is your suggestion about this problem?
Which component on the board damaged?
Was your power supply operating in constant current mode?
In other words, if you set the voltage and current limiters of your power supply to specific setpoints but the load exceeds that current, the power supply will compensate the excess current by reducing the output voltage. At this point the correct course of action is to increase the current limiter knob/potentiometer until the setpoint is set above the load current, allowing the power supply to operate in constant voltage mode.
One common mistake is to confuse the two (sometimes four) potentiometers of the power supply and inadvertently move the voltage limiter setpoint above the rated voltage of the equipment. This has no effect in the output of the power supply if it is operating in constant current mode, but it is dangerous if the load changes as the output voltage will increase.
In your scenario I think that might have happened. When the DMM had an increased load of a discharged battery, the power supply might have been operating in constant current mode. The moment you removed the battery, the load decreased and the voltage increased as the current limiter was set "free". This might have damaged your DMM, even with an input voltage regulator.
Unfortunately I don't have this meter and therefore can't provide much more information about its repair.