Symptoms
In the current version of K2 software (4.6.11 and earlier versions) out of box "Out of office" functionality does not send email notifications to delegates (forwarded users).
This is something you may try to address with custom solutions at the moment. But while trying to build solution which expand K2 OOF functionality so that it will send notifications additionally to delegates (forwarded users) as opposed to sending them only to task owner which is current behavior out of the box, you may need a way to programmatically generate emails with the same template as generic OOF email in runtime, which requires passing template ID parameter during runtime.
Diagnoses
For this scenario you would want to generate emails for forwarded users using the same template as generic OOF email. Normally you specify email event template in design time as inline function parameter which specifies path to template, but currently you unable to do this programmatically via K2 API (namely you cannot pass design time parameters during runtime). There is no plain and straightforward way to accomplish this using K2 API.
Resolution
There is an existing feature request to implement this functionality out of the box which is bound to be implemented post 4.6.11 release (this is subject to change).
Current OOF behavior is that notifications are sent to the destination user(s) of a task only. The secondary user is simply delegated permission to access and action the task item. The ownership of the task still flows to the original destination user, which does not change based on Out of Office rules. As a workaround One coupling K2's Out of Office function with Outlook/Exchange Out of Office to forward messages to the relevant user can be considered.
There is an existing coldfix for K2 4.6.9 which enables delegates (forwarded users) to receive task notifications. This colfix has the following limitation: irrespectively of your notification configuration (default/custom) client will always receive default notification with this coldfix.