How to Preserve Shared AMIs in the Target Account While Deleting it from the Source Account

Hello.

If you delete the AMI in the sharing source account, you will no longer be able to view it in the sharing destination account.
Therefore, after sharing the AMI, please copy the AMI in the sharing destination account.
By doing so, even if you delete the AMI in the sharing source account, the AMI will be available in the sharing destination account.
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/CopyingAMIs.html