Firstly, I found of high interest your question, so I followed myself a little bit the State of the Art. There is a huge literature on the subject the coating of copper onto carbon fibers by electroless deposition, by CVD (chemical vapor deposition) method, other techniques...
Here there are only some pieces of information that can help you (more or less):
- B. Bhav Singh, M. Balasubramanian, Processing and properties of copper-coated carbon fibre reinforced aluminium alloy composites, Journal of Materials Processing Technology, 209 (2009) 2104-2110.
- “Copper coated carbon fiber reinforced plastics for high and ultra high vacuum applications” see you: http://arxiv.org/pdf/1308.2563.pdf
- S. Kim, S. Kim, Y. Kim, B.-C. Ku, Y. Jeong, Enhancement of electrical conductivity of carbon nanotube fibers by copper sulfide plating, Fibers Polym, 16 (2015) 769-773.
- Z. Zhu, X. Kuang, G. Carotenuto, L. Nicolais, Fabrication and properties of carbon fibre-reinforced copper composite by controlled three-step electrodeposition, J Mater Sci, 32 (1997) 1061-1067.
- H. Cho, I. Tabata, K. Hisada, K. Hirogaki, T. Hori, Characterization of copper-plated conductive fibers after pretreatment with supercritical carbon dioxide and surface modification using Lyocell fiber, Textile Research Journal, 83 (2013) 780-793.
- Copper plating process on carbon fiber (CN1094100 A), Google Patents, 1994
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Good luck in the finding of the most helpfully answer and best regards,