What does social security in different places need to move into Fushun?

Moving insurance has nothing to do with hukou and files.

If you want to move to Fushun, as long as you have a company in Fushun, the company can also pay insurance.

Take your ID card to the local social security bureau to open a transfer slip and print the payment voucher. Take it to Fushun and hand it over to the person in charge of the unit. Someone else will take care of it for you.

If Fushun has no unit, it can't be transferred for the time being.

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