Move AWS EC2 Instance to another account
To share or migrate EC2 instances from a source account to a target account follow these steps:
Create a custom Amazon Machine Image (AMI) from the instance you want to share or migrate. Be sure to include all required EBS data volumes in the AMI.
Note: Data stored on instance store volumes isn't preserved in AMIs, and won't be on the instance store volumes of the instances that you launch from the AMI.
Share the AMI with the target account using either the EC2 console or the AWS Command Line Interface (CLI).
From the target account, find the AMI using the EC2 console or the AWS CLI.
Launch a new instance from the shared AMI on the target account.
Note: The private IP address of VPC instances will be different in the new account, unless you specifically set them during launch.
Related information
Changing the Encryption State of Your Data
AWS CLI Command Reference (EC2)
Source: Transfer Amazon EC2 Instance
The short answer is: No, you cannot move an running instance from one account to another unless and ofcourse AWS Technical support has some magic available behind the curtains.
You can However, Create an AMI from this instance and share this AMI with other users/account. refer: http://aws.amazon.com/articles/530