Connect:

Import-Module ExchangeOnlineManagement
Connect-ExchangeOnline -UserPrincipalName admin@tenant.onmicrosoft.com

From Alias to Shared:

Set-Mailbox Mailbox@domain.com -EmailAddresses @{Remove='Alias@domain.com'}
Start-Sleep -Seconds 60
New-Mailbox -Shared -Name "Alias Name" -DisplayName "Alias DisplayName" -Alias "Alias@domain.com"
Start-Sleep -Seconds 60
Set-MailboxRegionalConfiguration -Identity "Alias@domain.com" -Language nl-nl -LocalizeDefaultFolderName -TimeZone "W. Europe Standard Time"
Add-MailboxPermission -Identity Alias@domain.com -AccessRights FullAccess -InheritanceType All -AutoMapping:$true -User User@domain.com
Add-RecipientPermission -Identity Alias@domain.com -AccessRights SendAs -Confirm:$false -Trustee User@domain.com