In Sinch documentation for Android there's:
Note: Messages are stored in the backend for 30 days before being removed. If the recipient has not started the app and downloaded the message history within this time frame, the message will be lost and no notification will be received.
How storing messages is handled by Sinch or how should it be done to download the message history?
By logging in as the user, any unseen message on that device will automatically be downloaded. At the moment there is no public API to get the message history.