Hi,
check the settings of the your Item category and schedule line line category you are using in these transactions,may be you are using TAS and CS
The standard Third party scenario will not fulfill your requirement as the Dispatch of the materials are being done by the third party and not your company so automatically the account assignment settings will be different.
i think in the whole process you only require to generate a PR from the sales order and the remaining process need to proceed as a normal sales process like dispatch from your company