Yes, you heard it right, Dual-write mapping is solution aware meaning it can be exported from one environment and can be imported into another with the help of our beloved solutions.
The process of adding the Table mapping to a solution is straightforward.
In this blog, we will explore the process of adding the Table mapping to a solution as well as after importing the solution to the destination environment we will see how to use the latest version of the mapping.
Will be changing the CDS sales quotation header (quotes) table map (this comes along with the installation of Dual-write solutions) and save it with a different (higher) version and a publisher. (This blog will concentrate on moving the table mapping from one environment to another and after that on applying the latest version and will not cover the steps on how to change an existing table mapping)
Before Changes:

After Changes:

Steps on adding the Dual-write (Table) Mapping to a solution:
Navigate to https://make.powerapps.com. From the top right-hand side corner choose the right Environment and go to the Solutions tab.

Open the solution in which you want to add the mapping (or create a new if you do not have one).
Click Add existing -> More -> Other -> Dual Write table map

From the Add existing dual write table maps screen, search for the table mapping name and then select the right mapping and click Add.

Note: If you are adding the table mapping in an existing solution and the table mapping in question already exists with an older version then kindly remove the older mapping from the solution first and then add the new one.
Next step is to export the solution (preferably managed if moving to a Production environment) and import it in the target environment.
Once the solution is imported, it is time to look at how to use the latest table mapping.
Steps for enabling the latest table mapping:
In the Dual-write module click on Apply Solution.

In the Apply Solution screen select your solution and click on Apply.

Search for the Table Map then select the Table map from the list and click on Table map version.

Select the right Table map and click Save. Voila!!!

Conclusion:
It is easy to move the table map from one environment to another.
In the next blogpost, I have discussed in detail about the Dual-write Integration Key.