Think it is a synthetic somewhat ( spinel, corundum) - a synthetic tourmaline doesn't make sense ( to expensive) - the tourmaline group has a very complicated chemistry.
The stone weights 3,7 ct - we would know it if there is synthetic tourmaline in the market.
I will send an email to the vendor. Google synthetic tourmaline, gia or agl or other labs, organisations - they would know it before a custom cutter in sweden is able to purchase and cut a rough item large enough for a 3,7 ct gem.
There was experimental syth. tourmaline - small, expensive.
And "synthetic tourmaline" is NOT synthetic spinel colored like tourmaline. This would be misleading and unprofessional.