Can you Transfer an EC2 Instance to another AWS Account
You cannot transfer an EC2 instance (or any other resources) to a different AWS account.
If the instance is EBS boot (recommended), you might try an approach like this:
Stop the current instance (ec2-stop-instances)
Create an AMI from the instance (ec2-register-image)
Give the second AWS account permission to run that AMI (ec2-modify-image-attribute)
Run a new instance of the AMI under the second AWS account (ec2-run-instances)
DNS would need to be updated to point to the IP address of the new instance (preferably using an Elastic IP Address). Any other AWS/EC2 resources would also need to be copied/recreated in the second account.
After sufficient testing, you might want to free up the original instance (ec2-terminate-instances).
The second account should create their own snapshots / AMIs of the instance to protect themselves if their instance/EBS volume fails after the AMI owned by you is deleted.
Even better, you should have documented/scripted exactly how your instance was created so that the client can reproduce this at will.