How to transfer Shanghai social security to Wuxi

Of course you can. First go through the social security transfer formalities at the local social security bureau in Shanghai. The Social Security Bureau will give you a form, then make a social security bill and send you a social security transfer letter. You go to the local social security bureau where you work in Jiangsu to apply for a social security account, and then give your ID card and all the information given by Jiangsu Social Security Bureau to Jiangsu Social Security Bureau. Upon completion, Jiangsu Social Security Bureau will give you a letter with a bank account number on it. You take this letter to Shanghai Social Security, and the Shanghai Social Security Bureau will transfer the personal contribution of your social security to. Some troubles, need to run at both ends, be prepared.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.