Sorry for the delay in response.
There is no direct option to save the scanned PDF to the local storage.
However, you may use the workaround mentioned below to save the file locally.
a) Using browser
-Open this link https://cloud.acrobat.com/ on a browser on your device and Sign in with your Adobe ID.
- Then go to Files > Document Cloud > Adobe Scan folder.
- Select the file from the list and download it on your device.
b) Using Mail
- Open the PDF in Adobe Scan app.
- Then click on the Share icon at the bottom.
- Select "Share a copy" from the options provided.
- Select Mail and send an email to yourself.
- Then open your mail and download the document from there.
Hope that helps.
Let us know if you have any questions.