Typically, such cracks are repaired with a mixture of sawdust and cyanoacrylate, preferably
sawdust of the same type of wood as the instrument.
I can’t tell for sure what wood that is. It is not the African Blackwood that might be expected, but maybe something in the same family. It looks rosewoodish, but wood
identification from grain alone is exceedingly tricky and I’m not claiming to be an expert.
You may want to get the crack repaired by a professional.