There is less need for backups in Telegram, because your chats are stored encrypted in the Telegram Cloud — and you can access them from any of your devices anytime. Secret Chats are the only exception to this rule: they are only available on their device of origin and are lost when you log out.
Telegram Web (web.telegram.org) together with a web browser which supports printing as .PDF (e.g. Google Chrome), allows you to export your chats.
Telegram Web quick steps
- Open Telegram Web and login
- Mark the conversation (see screenshot)
- Open print dialog box and select 'selection only' (see screenshot)
- Launch Google Chrome on a computer
- Login to web.telegram.org
- Select the Cloud Chat you want to export
- Click on the chat area so you can scroll through the chat history using your keyboard
- Hold down the HOME button on keyboard to scroll to the beginning of the Chat History (this may take a while for large chats). This step will allow you to easily select all text later.
- When you reach the beginning of the Chat History, press the END button on keyboard to go back to the bottom of the chat.
- Drag your mouse to highlight the most current section of the chat, from bottom to top.
- With the highlighted text starting at the bottom of the chat, press CONTROL + SHIFT + HOME buttons. This will automatically select the rest of the entire Chat History, all the way to the very beginning.
- Right click > "Print"
- Change Destination to 'Save as PDF'
- Enable Background graphics and Selection only (Background graphics may allow displaying emoji)
- Click the SAVE button to export to a PDF file
You will now have a text searchable PDF export of your Cloud Chat History.
There are also scripts (created by other Telegram users) which claim to be able to download all chats. Keep in mind that you may easily run into a flood limit (not possible to use the account for some time) or worse: risk, that the script creator is able to see all your private chats.