If I use user interface Tools – Domain mapping (changeing last to first url)
Would result in broken images.
Based on http://codex.wordpress.org/Moving_WordPress I would assume, it makes sense to use https://interconnectit.com/products/search-and-replace-for-wordpress-databases/. My question is : Is there a better way to change domain mapping so that it does not result in broken images.
When I have changed domain before on a single site installation I have used the database find and replace method (always backup first!) and I’ve found this to work sufficiently for that.
If you want an alternative you could use rewrites for the old domain to point to the correct files for the images.
There has been some info posted here in regards to rewrites for a similar issue https://wordpress.stackexchange.com/questions/53873/host-wp-content-on-other-domain-much-like-a-cdn#answer-53881
Just redirect any request from the old domain for images to the correct folder. This will however require you to keep the original domain for the foreseeable future.
You can find info on all the WordPress rewrites here http://codex.wordpress.org/htaccess
I hope this answers your question