Who finally ended Salem witch trails?

Answer 1

Governor William Phips, who first authorized the trials, was later influenced by writings of Increase Mather (father of Cotton Mather) and Samuel Willard questioning the fairness of the trials, brought the trials to an end in September 1692 when it became clear that the trials were injust and specious.

This did not end acrimony and accusations. The governor's wife was accused of witchcraft at one point, by then all such charges were being ignored or thrown out. It was likely the wife was accused because the governor had already stopped the trials and had released the remaining who were jailed or condemned.

Answer 2

Governor Phips stopped the trials when his wife was accused, but he could not official declare all the accused innocent without permission from King William and Parliment. When Parliment sent the letter giving him the power to do that, he could. So it was both Phips and the English government.