Yes, that’s pretty much a direct quote from the Pali suttas. The passage is in DN 28:
Purisassa ca viññāṇasotaṃ pajānāti, ubhayato abbocchinnaṃ idha loke patiṭṭhitañca paraloke patiṭṭhitañca
They understand a person’s stream of consciousness, unbroken on both sides, established in both this world and the next.
“Mindstream” would be a pretty good rendering, though!