Disabling an AD account is not instant so the best was is to disable the services for the user :

(It can take around 5-10 minutes for the disabling of the protocols and/or settings to go into effect ) 

For Exchange 2007: Set-CASMailbox -Identity <user> -OwaEnabled $false

Set-CASMailbox -Identity <user> -MapiEnabled $false

Set-CASMailbox -Identity <user> -MapiBlockOutlookRpcHttp $true

Set-CASMailbox -Identity <user> -OwaEnabled $false

 For Exchange 2010, 2013, 2016 and 365:Set-CASMailbox -Identity <user> -OwaEnabled $false

Set-CASMailbox -Identity <user> -EwsEnabled $false

Set-CASMailbox -Identity <user> -EwsEnabled $false

Set-CASMailbox -Identity <user> -EcpEnabled $fals

Set-CASMailbox -Identity <user> -MapiEnabled $false

Set-CASMailbox -Identity <user> -MapiBlockOutlookRpcHttp $true

Set-CASMailbox -Identity <user> -EwsAllowMacOutlook $false

Set-CASMailbox -Identity <user> -EwsAllowOutlook $false

You might want to set an Out of Office on for the user if needed for external parties, and also arrange email forwarding to a colleague and access to the mailbox for previous mail

Then Disable AD account!