Encrypted messages are stored on their servers only until they are delivered, and then deleted. From their privacy policy: Messages. Signal cannot decrypt

Encrypted messages are stored on their servers only until they are delivered, and then deleted. From their privacy policy: Messages. Signal cannot decrypt or otherwise access the content of your messages or calls. Signal queues end-to-end encrypted messages on its servers for delivery to devices that are temporarily offline (e.g. a phone whose battery has died). Your message history is stored on your own devices. Additional technical information is stored on our servers, including randomly generated authentication tokens, keys, push tokens, and other material that is necessary to establish calls and transmit messages. Signal limits this additional technical information to the minimum required to operate the Services.