Doing Business in China
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A Hong Kong company cannot issue mainland invoices (fa piao). So that will not help you solve the problem.
The simple but slightly risky solution is to ask someone to do this for you, i.e. issue a fa piao in the name of their company, collect the money, then hand the money over to you after deducting taxes incurred and any service charge for offering this help.
What kind of graphic designing do you do? I might be able to use your services. Pls email me at thomasw98 "at" gmail.com