Under the environment of energy sharing between prosumers in power distribution systems, unified pricing, and transactions bring challenges to clarify the additional environmental value of heterogeneous electricity. This is not conducive to a low-carbon transition of end-prosumers and the sustainable development of distributed renewable energy. Therefore, an energy-sharing strategy for a green local energy market (LEM), which considers carbon credit and power traceability, is proposed. A carbon credit is used to monetize the environmental cost of heterogeneous electricity and circulate it together with it in the LEM. To minimize the energy and carbon credit cost of all prosumers/, an electricity-carbon credit joint clearing model is established, and a traceability-based pricing method for heterogeneous electricity is proposed to encourage prosumers to conduct their energy management in a low-carbon way. Using the alternating direction method of multipliers (ADMM), the proposed model is solved in a distributed manner via limited information exchange, thus realizing a distributed energy management of the green LEM. The case studies’ results verify the proposed strategy's effectiveness in reducing the total energy cost of the green LEM and promoting green substitution in terminal energy consumption.