Modification to Magento 1.9.3.2 code required to integrate with Unleashed saas system

We're migrating to a new saas stock management system called Unleashed (https://unleashedsoftware.com). Unleashed integrates with Magento in order to sync stock levels and order status updates etc.
Unleashed have told us that their software is not compatible with Magento Community 1.9.3.x and that a change is required to the code in order to make it work. We're running on Community 1.9.3.2.

Unleashed have pointed us to a help doc on their website that covers their Magento integration: http://help.unleashedsoftware.com/magento-integration
This doc links to a conversation on Stack Exchange that discusses the underlying issue which seems to relate to connections via a SOAP/XML-RPC user: https://magento.stackexchange.com/questions/140761/soap-connection-problems-after-1-9-3-0-update/
The conversation isn't specifically about Unleashed but I believe the solution offered up here will also resolve connection issues with Unleashed.

Aside from amending the code as discussed, we require the developer to test and demonstrate that the work they have carried out works and allows for Unleashed to integrate fully with our version of Magento.