The global market for End of Life Lithium-Ion Batteries is growing exponentially to satisfy the needs of electric mobility and clean energy technologies. Reusing or repurposing these batteries could ensure sustainability and keep the excessive demands of raw materials in check. However, a strong commitment and trust from the various stakeholders is necessary to build such circular industrial systems. In this paper, a thorough analysis of practices and regulations allowed us to highlight the actors and processes involved in the life cycle of repurposed Lithium-Ion Batteries (LIBs). This led us to propose a conceptual framework describing a generic organization for LIB repurposing. LIB State of Health and diagnosis estimations, which can be carried out with data from LIB passports, are also underlined as essential for the functioning of the organization. This was discussed and implemented on a real case of LIBs used as a power source for electric heaters after their first life in a mobility application.