I also found this on another website, just to supplement further on what Namdrol has posted :
Meeting Between Shunzhi and the Dalai Lama
Toward the end of 1652, or the ninth year of the reign of Emperor Shunzhi, the fifth Dalai Lama reached Beijing, where he was given a rousing welcome by Emperor Shunzhi and court officials. The Qing court built the Huangsi Monastery especially for him to live in during his two-month stay, and Emperor Shunzhi hosted a feast for him in the Hall of Grand Harmony in the Forbidden City. In the spring of 1653, when the fifth Dalai Lama left for Tibet, Emperor Shunzhi gave him handsome gifts, including 550 taels of gold, 12,000 taels of silver and 100 bolts of silk. The empress dowager gave him 100 taels of gold, 1,000 taels of silver and 1,000 bolts of silk. The emperor also granted him an honorific title, a golden certificate of appointment and a golden seal of authority. This established a precedent for the Dalai Lama of later generations to receive their post offically from the imperial court. [1]
The text of the golden certificate of appointment which Emperor Shunzhi gave to the fifth Dalai Lama read in part:
"I was told one who has good luck strives to do things in favor of others while one who suffers from frustration pays more attention to self-cultivation. They do things in a different way. Whether one takes official post or enters monkhood takes the same road. You, the Dalai Lama, are broad-minded and boast boundless beneficence, striving to cultivate both samadhi and mati. Casting away sunya, you concentrate yourself on spreading Buddhist teachings among ignorant populace. So, Buddhism flourishes in the west and enjoys good fame in the east. Emperor Taizong was so glad to know all these that he sent a special envoy to invite you to the court. Reading the mind of the Heaven, you promised to come in 1652. When I came to power upon the will of the Heaven, you did come. Your performance here shows you have attained the realm of prajna. I appreciate your efforts to enlighten people, which should be taken as the steps leading to the top of the mountain and the boat that carries people across the sea. I hereby grant you the golden certificate of appointment and the golden seal of authority, making you the Dalai Lama, Overseer of the Buddhist Faith on Earth Under the Great Benevolent Self-Subsisting Buddha of Western Paradise." (The Records of Qing Dynasty Emperor Shizong, Vol. 74, 18)
The text of the golden seal of authority which Emperor Shunzhi issued to the fifth Dalai Lama reads: "The Dalai Lama, Overseer of the Buddhist Faith on Earth Under the Great Benevolent Self-Subsisting Buddha of Western Paradise." (The Records of Qing Emperor Shizong, Vol. 74, 18)
It seems that there had always been a long standing relationship between the emperors of China and the Dalai Lama since the Great fifth. Buddhism had flourished and I agreed with what HopeRainbow has just mentioned, even HH the 14th Dalai Lama is promoting Buddhism in China, contrary to what people may think otheriwse. Irrespective with the current political wind which does not seem to be in favour for the Dalai Lama to spread Buddhism in China personally, the Dorje Shugden ban initiated by the Dalai Lama has indirectly working its effect in China, Dorje Shugden's practice is spreading as can be seen by many DS monasteries built in China.