On the AlphaGrowth recorded space page, find the audio “Player” section and click on the three dot menu at the far right of it. A drop down menu with the “Download” option will pop-up, once you click it the recorded space will be downloaded to your device.
Twitter Spaces can be recorded on Twitter by the host. In addition, there are companies that record and store Twitter Spaces, for example, you can find Twitter Spaces recordings on AlphaGrowth and you can listen, download, or read transcribed Twitter Spaces. You can access Twitter Space recordings here.
You can find recorded Twitter Spaces on the Spaces host Twitter feed. Alternatively, you can go to the AlphaGrowth Spaces page and find, listen and download recorded Twitter spaces from there.