No.397248
China didn't annex Tibet directly. It was the Mongols in the 13th century who annexed it. They were eventually beaten by the Ming Dynasty in the 14th century, and the Ming inherited some kingdoms that had never been part of China, such as Tibet. The Qing Dynasty replaced the Ming, then the Republic of China replaced the Qing in 1912. The People's Republic of China replaced the ROC in 1949, mostly, with the remaining part of the ROC still sitting in Taiwan. Tibet has been part of this line of succession.
One detour though is during the Century of Humiliation when the British managed to sneak around in Tibet, and on paper, Tibet maintained a degree of autonomy until 1950. But that doesn't mean Tibet was living in peace and prosperity. On the contrary, the Tibetan economy was near collapse as it was based on slavery with a theocratic political system characterized by bloody power struggles between Lamas, similar in many ways to Han warlord zones in the rest of China.
Eventually, in 1951, the PRC restored China's de jure sovereign rights in Tibet using both peaceful and non-peaceful measures. And, at least on paper, it was still a part of the ROC and recognized as such by the international community until the normalization of relations with the PRC and the rest of the world, which then legitimized the PRC's move on Tibet. And if there are any Buddhists who disagree with any of this, they're free to abolish the current Dalai Lama because he was born in Qinghai (not Tibet) and his legitimacy was granted by the ROC according to the ancient tradition that the Chinese "emperor" was a reincarnation of a Bodhisattva.