But it must be in the name of the unit first enrollment. The procedure is to bring your ID card and social security card to the social insurance agency in Zhejiang to open the "pension insurance payment voucher" and "medical insurance payment voucher", and then, after enrolling in Shanghai, you will give the two payment vouchers to the social insurance agency in Shanghai to apply for the transfer.
If you are a girl and really don't have a unit to participate in the insurance, there is another way to continue to pay social security in Zhejiang, the back can be married to Shanghai, sooner or later, you will get the Shanghai hukou (as long as before the statutory retirement age), and so on to get the Shanghai hukou and then apply for the transfer of insurance procedures.