Configuring Teams calendar access for Exchange on-premises mailboxes

Frank, thank you so much for your reply.

You confirmed my suspicious that the cause is probably in the on premise Exchange. I was trying to enable the  room account with the command "Enable-Mailbox babeta -room" but that threw an error:

Enable-Mailbox : This task does not support recipients of this type. The specified recipient babeta is of type UserMailbox. Please make sure that this recipient matc
hes the required recipient type for this task.

Also I tried to enable it with command "Set-Mailbox babeta -EnableRoomMailboxAccount $true -RoomMailboxPassword (ConvertTo-SecureString -String 'pass' -AsPlainText -Force)" which resulted in an error:

Set-Mailbox : You don't have permission to directly change a mailbox account password without providing old password. Reset Password role is required for directly changing password.

But I do have the Reset Password role assigned to the use under which I run the command.

So, yes, I think this condition of the account is not OK:

Get-Mailbox babeta | fl IsMailboxEnabled,RoomMailboxAccountEnabled,AccountDisabled,ExchangeUserAccountControl,accountdisabled

IsMailboxEnabled : True
RoomMailboxAccountEnabled : False
AccountDisabled : True
ExchangeUserAccountControl : AccountDisabled
AccountDisabled : True

It shoudl be like this (a new account which I created directly with "-EnableRoomMailboxAccount $true"):

Get-Mailbox jawa | fl IsMailboxEnabled,RoomMailboxAccountEnabled,AccountDisabled,ExchangeUserAccountControl,accountdisabledIsMailboxEnabled : True
RoomMailboxAccountEnabled : True
AccountDisabled : False
ExchangeUserAccountControl : None
AccountDisabled : False

But I am not able to change the existing account.

Petr