That bit is not true. Neither the republic of India or Pakistan existed when the Taj was built, but as of today it is located in the Republic of India, and is a property of the govt of India, who's responsibility it is to maintain and protect it. If the question is whether the architectural accomplishment is Indian or Pakistani, the question is invalid, as neither entities existed back then. But if the question is about who's property it is today, it is very much India's. It is Indian governmental property.It's part of our history, but it's nothing to do with the state of Pakistan that exists today, with that said, it has almost equally less to do with today's republic of India too. Neither of which existed back then.
By the way I forget who, but somebody had described it as the ''soul of Persia in the heart of India'', and was quoted in the 'Discovery of India' by Jawaharlal Nehru. ''India'' in that quote obviously referring to the undivided India of that time, not present day republic of India.