Lime Green Turquoise & Branch Coral – Help with ID

I purchased a broken vintage necklace at a yard sale.  I was told the red pieces were branch coral (which I believed was so) and the long green “tooth like” piece were lime turquoise (which I understand is rare).  Based on comparisons I’ve done with lime green turquoise imposters ie; chrysoprase, gaspetite, variscite) the inside of the stone (a few were broken – see photos) does not look like the imposter stones.  I can not find a photo of an inside cut piece of lime turquoise to compare.  The inside color is completely and evenly the same as the outside – i do not believe it was died but I am not an expert.  If anyone can help let me know what I have I would appreciate it.  Thanks Rick