As compute requirements in experimental high-energy physics are expected to significantly increase, there is a need for leveraging high-performance computing (HPC) resources. However, HPC systems are currently organised and operated in a way that this is not easily possible. Here we will focus on a specific e-infrastructure that incorporates HPC resources, namely Fenix, which is based on a consortium of 6 leading European supercomputing centres. Fenix was initiated through the Human Brain Project (HBP) but also provides resources to other research communities in Europe. The Fenix sites are integrated into a common AAI and provide a so-called Archival Data Repository that can be accessed through a Swift API. In this paper, we report on our efforts to realise a data transfer service that allow to exchange data with the Fenix e-infrastructure. This has been enabled by implementing support of Swift in FTS3 and related software components. We will, in particular, discuss how FTS3 has been integrated into the Fenix AAI, which largely follows the architectural principles of the European Open Science Cloud (EOSC). Furthermore, we show how end-users can use this service through a WebFTS service that has been integrated into the science gateway of the HBP, which is also known as the HBP Collaboratory. Finally, we discuss how transfer commands can be automatically distributed over several FTS3 instances to optimise transfer between different Fenix sites.