After the tragedy there was only one person left to trust, so Sirius wrote his account of the recent events and tied them to the leg of his owl. He expected to be killed the next day, but at least his friend would know the truth, and might understand why he had been left alone again.
The owl searched for two days before finding him, by which time the full moon had risen. The ancient compulsion forced the owl onwards, delivering the message into the jaws of the wolf.
In the morning, Remus had no memory of owl or parchment.