I mean... They are different people, but the same soul. So the whole soulmates thing should mean that they are meant to be together no matter how their lives turn out. But I do prefer when the immortal falls in love with a different person (not a reincarnation) after a long period of grief.
If you've watched Inuyasha, I love how the whole reincarnation thing is treated there. It perfectly summarises the different people situation.
Omg inuyasha. I missed them. Gotta rewatch
Omg inuyasha mentioned. I missed them. Gotta rewatch
The double reply omfg sorry
I always hate the ' in his next life I will love him again trope ' because to me that's two different people