So I understand that if I want to notify about something to another pool, I can have a task named "notify client about succesful purchase". My question is, what happens when I want to send a notification among lanes?
For example if in the same pool I have a seller and an supervisor, and the seller has to notify the administrator that there is an order on the way. Can this be a task? or in a pool you don't have to notify anything and just draw the flow of the process's entity (in this case the order)?
A Message Flow MUST connect two separate Pools. They connect either to the Pool boundary or to Flow Objects within the Pool boundary. They MUST NOT connect two objects within the same Pool.
A Send Task is a simple Task that is designed to send a Message to an external Participant (relative to the Process).
Based on the above excerpts taken from the BPMN 2.0 specification by Object Management Group, we cannot use either message flows or Send Task to represent the message communication within the process pool. Hence, my recommendation would be to use a simple System task "Notify Administrator"
Also, I would use a task than a "throw intermediate message event" because I understand from your requirement that notifying the administrator has to be done always, hence this becomes a task in the process than an event that may or may not happen.