One solution:
(Note this will not work on a domain controller as they do not differentiate between AD and Local logins on a domain controller)
- Create a local user on Computer A ie ComputerA\SharedServiceUser
- Create a local user on Computer B with exactly the same username and password ie ComputerB\SharedServiceUser
- Set permissions on the share on Computer B for the local user created on ComputerB
- Set the service on ComputerA to run as the local user on ComputerA
This works because windows password hashes don't salt. So when the service on ComputerA passes its identity across the network as .\SharedServiceUser with Hash as password it matches the local user identity on ComputerB .\SharedServiceUser