Consider that I have got a AWS account that already has some parameter store data.
Is there a way to migrate these data from this parameter store to another:
I would prefer official tools to do this, but tools similar to dynamoDB dump are also welcome.
There is no "official tool" to do this. It could be done by iterating through the existing parameters and creating them in the target.
I found this tool that somebody has written: aws-ssm-copy · PyPI: Copy parameters from a AWS parameter store to another
It looks like it can copy between Regions and between AWS Accounts (by providing multiple Profiles).