come around to (someone's) point of view

Translations
принять чью-либо точку зрения
He was initially opposed to the idea but soon came around to her point of view.
Поначалу он был против этой идеи, но вскоре принял ее точку зрения.
Definitions
To change one's opinion or perspective so that it agrees with someone else's; to be persuaded to accept or support another person's viewpoint.