I want to restore a mail which we delete using Microsoft graph api.
I don't find any api to restore or recoved a deleted mail using apis.
There is no restore method in the Graph API (there also isn't one in MAPI or EWS). When an Item gets deleted in Exchange it just gets moved into another folder in the Mailbox up until the time the retention period of the Item expires then the MFA(Managed Folder Assistant) deletes the Items.
So for example to restore an Item that was in the dumpster you would need to query for the Item in the dumpster like
https://graph.microsoft.com/v1.0/users('[email protected]')/MailFolders/recoverableitemsDeletions/messages/
Then you could move it back into what ever folder you want using https://learn.microsoft.com/en-us/graph/api/message-move?view=graph-rest-1.0&tabs=http
If you wanted to move it back to the original location it was deleted from you would need to use the LAPFID (Last Active Parent FolderId) property https://blogs.technet.microsoft.com/exchange/2017/06/13/announcing-original-folder-item-recovery/ . Eg to get that on items in the dumpster use
https://graph.microsoft.com/v1.0/users('[email protected]')/MailFolders/recoverableitemsDeletions/messages/?$select=Subject&$Top=10&$expand=SingleValueExtendedProperties($filter%3DId%20eq%20'Binary%200x348A')
Using the LAPFID is a little tricky as it's only a partial folderId so you need extra code for that, there are a few examples of using it in https://gsexdev.blogspot.com/2018/10/using-lapfid-last-active-parent.html