Yes, interspecies adoptions have been observed. They're rare enough that study is limited to case reports, and the causes are guessed at but not fully understood. However, I think it's clear that there are strong biological drives towards participating in mothering for the species that do so, and it's not too surprising that these drives could be at times "misplaced" from a biological perspective and directed at non-offspring.
A couple papers:
Carzon, P., Delfour, F., Dudzinski, K., Oremus, M., & Clua, É. (2019). Cross‐genus adoptions in delphinids: One example with taxonomic discussion. Ethology, 125(9), 669-676.
Izar, P., Verderane, M. P., Visalberghi, E., Ottoni, E. B., Gomes De Oliveira, M., Shirley, J., & Fragaszy, D. (2006). Cross‐genus adoption of a marmoset (Callithrix jacchus) by wild capuchin monkeys (Cebus libidinosus): Case report. American Journal of Primatology: Official Journal of the American Society of Primatologists, 68(7), 692-700.