Is there an invoice for the purchase tax paid by Jiaxing 4s shop?

Yes

You can query, download and print electronic invoices through electronic tax bureaus all over the country. After you pay the purchase tax, the IRS will give you a purchase tax invoice. The vehicle purchase tax is not given to the 4S shop, and the 4S shop has no right to collect taxes. The 4S shop is only an agent and finally pays the vehicle purchase tax to the local national tax authorities, and the 4S shop staff only handles it on its behalf.

The vehicle purchase tax invoice shall be issued by the tax bureau that pays the vehicle purchase tax. After the vehicle purchase tax is paid, the system will automatically issue a purchase tax invoice. However, instead of issuing a paper-based vehicle purchase tax invoice, only an electronic vehicle purchase tax invoice is issued, that is, a vehicle purchase tax payment certificate (electronic version) is issued.