The social security I bought before has not changed. Can I buy it anywhere else?

You can reapply. No matter how long you have paid in the original place, it is new to social security to submit it after you arrive in other provinces. After you successfully apply for social security in your new local unit, you can transfer the social security of your old place to your present place. But you need to go to the former social security bureau to go through some formalities and get the materials.

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