[GekkePrutser]

Signal does store stuff if you have desktop clients logged in. It doesn't rely on the mobile client to forward it like Whatsapp Web. But it only stores it until they have all retrieved it, or they have timed out. I don't know how long Telegram keeps stuff.

[newscracker]

Desktop client or phone client or tablet client, Signal will store the messages on its servers for several days or until they’re delivered, whichever is earlier.