According to the information you provided, it is difficult to judge whether the Lantian jade bracelet given by a friend is really valuable 1600 yuan. Therefore, the following are some suggestions:

1. Check the appraisal certificate: make sure that the certificate is issued by an authoritative organization or a professional appraisal institution. The appraisal certificate should contain detailed information of the bracelet, such as material, color, weight and so on.

2. Know the market price: Before judging the value of Lantian jade bracelet, you can know the market price. With reference to some market prices in lantian jade, combined with the quality, technology, color and other factors of bracelets, roughly estimate the price of bracelets.

3. Appearance inspection: check the appearance of the bracelet and observe its color, transparency and texture. Lantian jade is generally blue or blue-green, slightly transparent to opaque, with delicate and hard texture.

4. Hardness test: Use Mohs hardness pen to test the hardness of bracelet. The hardness of lantian jade is generally between 4 and 5.

To sum up, the authenticity and value of Lantian jade bracelet cannot be determined by the information provided. If the value of the bracelet is in doubt, it is recommended to consult a professional jewelry appraisal institution or expert.