Continuing a discussion with @ljpp at our forum. Technically speaking the current description is ok, but otherwise I think it needs to be changed. I think that it is clumsy and can even be mislead a user to think that the badge is awarded on the first anniversary only.
This badge is granted when you’ve been a member for a year with at least one post in that year. Thank you for sticking around and contributing to our community. We couldn’t do it without you.
We ended up suggesting that the description should be changed to this.
This badge is granted annually to celebrate the anniversary of your membership, provided that you posted once or more during the past year. Thank you for sticking around and contributing to our community. We couldn’t do it without you.
I generally don’t agree with “anniversary” as the terminology here. Perhaps it could say
This badge is granted each year you’ve been a member with at least one post in that year. Thank you for sticking around and contributing to our community. We couldn’t do it without you.
But sure, feel free to change that copy on your instance via Admin, Customize.
We already made the local change for Finnish at our forum and I also made a more subtle refinement for the general Finnish locale.
The change you proposed clears any possible confusion, too. So it would be fine. I let native speakers decide what kind of change the English string needs.
This makes more sense than 
