This wikiHow teaches you how to download a video of a Telegram conversation and save it to your computer in the Telegram desktop application.
Steps

Step 1. Open the Telegram desktop application on your computer
The icon is a blue background with a white paper airplane inside. On Mac, it's in the Applications folder and on Windows, it's in the start menu.
To download and install the desktop version, go to the application page

Step 2. Click on a conversation in the left pane
Find and click the conversation that contains the video you want to save. The conversation will open on the right side.

Step 3. Right click on the video you want to save
Find the video in the conversation and double-click it to see the options. A drop-down menu will open.

Step 4. Click Save File As in the menu
This option will allow you to download the video and save it on your computer. Clicking on it will open a new window and you can select the destination folder to save it on your computer.

Step 5. Select a folder on your computer
Here you will find the video once the download is finished.

Step 6. Click Save in the drop-down menu
This will download and save the video in the selected folder.