come around to (someone's) way of thinking

Translations
согласиться с чьей-либо точкой зрения
After a long discussion, she finally came around to his way of thinking.
После долгих обсуждений она наконец-то согласилась с его точкой зрения.
Definitions
To gradually change your opinion or perspective so that it matches someone else's; to eventually agree with another person's viewpoint after initially disagreeing.