Can the social security paid in Wuxi be transferred to Jiangyin?

Yes, take your ID card and household registration book to the social security center in the area where your unit is located to handle the admission notice and social security bank account information (name and account number of the bank), then go to the social security center in the area where your unit is located in Wuxi to transfer it out, print a detailed list of payment for you, and finally continue here in Jiangyin.