1- Orphan elephants need to be given the same companionship as they would have received from their mothers in the wild.
2- Orphan elephants need to be given the same companionship as they should have received from their mothers in the wild.
Which is correct, please?
(IMO, the second is correct.)
The first is correct. Although it's true that they should have been allowed to continue to live with their mothers in the wild (ie their mothers should not have been killed), it's much more natural to refer to the companionship that they would have received had their mothers not been killed.
I would prefer "Orphaned elephants".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.