Try the server first, because Exchange may not have actually thrown the mailbox away yet. The server copy beats any recovery from cache.
Deleted mailboxes enter a retention period, thirty days by default on both Exchange Server and Exchange Online, during which an admin can reconnect or restore them intact. On premise that is the disconnected mailbox area, in 365 it is a soft deleted mailbox restorable through PowerShell or the admin center. Check how long ago the deletion happened before touching the laptop, inside the window this is a clean administrative restore with nothing lost.
Past the window, the OST on that laptop graduates from cache to sole surviving copy. It is genuinely recoverable: the file contains the mailbox as of its last sync, and a standalone converter reads it without the dead account, SysTools OST Converter parses the file directly and exports to PST for legal review or import into another mailbox.
Handle the laptop accordingly before anything else: image or copy the OST out via %localappdata%\Microsoft\Outlook without starting Outlook on it, since launching Outlook against a dead account can prompt profile changes that touch the file. Copy first, convert the copy and note the last sync time visible in the converted data since the recovered snapshot is only as current as the final sync before the laptop was returned.