since I do not like
After two unanswered questions (if not that of Amazon, "We sent your questions about GMC 823669 Edger ... to other customers who bought the product and product sellers, but unfortunately no of them has answered "), I finished my reel ... and found no trace of specific product advised by the manufacturer or seller.
I did find a resemblance with products for Black trimmers and deker or Ryobi (twisted 1.5mm blue) and bought (in MB ... because cheaper) lot 2 RAC109 coils; the wire is OK but although very similar coil prevents closing the lid. I got the wire and have rewound on the original coil (attention to the user manual schema is good, not the text that says to turn the reel in the direction of the arrows).
If necessary, it is possible to use coils Ryobi but deepening of about 1 mm central hole.