Hi
Can anyone tell me can we get a permanent apk file of app download. If yes then how?
When you get the email link, download the APK file and save it to any location you desire. If you plan to share it with others then you might save it in Google Drive and send the share link of it to whomever you want to use it.
Will it work if I share after 2-3 days?
After saving Google drive
As @muneer already sugetsted, once dowloaded an .apk file, its yours forever 
You can do it with it as you desire.
Availability its up to the storage you choose to upload it.
It will be available for you until you remove it from the drive.