The Actionstep system is hard coded to use the CLIENT by default as the payer of any bill raised. Sorry this can only be changed globally
However, when you raise the bill, you can change who the bill is sent to by clicking on the word CHANGE inside the bill
Then you will be able to select any contact in the database to send the invoice to.
** NOTE - This will only change it for just this not for any future bills raised on the matter.
If you did have a particular matter that required ongoing a would like something You can also add another Party role on each matter type called. "Third party payer" if you like as this will help to show who the bill will be paid by, but it will still default to Client and you will need to change it at billing time as detailed above.