We can share the RDS snapshots with other AWS accounts and this article explains the steps to achieve the same.
Step1: Login to AWS console.
Step2: Select the RDS management page.
Step3: Choose Snapshots from the menu and select the the snapshot that to be shared from the list.
Step4: Choose "Share snapshot" from Actions.
Step5: Specify the AWS account number to which the snapshot need to be shared and save the configuration.
Now the snapshot will be available in the other AWS account that we specified here.