my old site 'example.com' is now 'archive.example.com' and there are many absolute URLs of images on it, how can I use this feature of 'Admin Tools' to solve my problem?
In AdminTools set "Enable Link Migration" to Yes and then enter the old host name ie.
example.com (don't include
http:// at the front)
However this will not solve your problem.
The fastest way is to export the SQL database and to replace every instance of
http://archive.example.com and then reload the database. It only takes a few minutes
To do this on a CPanel site, use phpMyAdmin, click on the database in question, so it loads the structure, and then click Export. Make sure you select SQL, set compression to ZIP or GZIP (whatever archive extraction utility you use) and also "Add DROP TABLE..." to the settings and then download. Extract the file, and do the "find and replace" in a text editor and save it. (Zip it to save upload time and then in phpMyAdmin click Import and upload the file.
Test the site and ensure that the lnks have changed correctly. If you screw up you can always reload the archive of the original database, or redo the process using a fresh version and be a bit more careful with what you change.
In the future, use relative links in your Joomla articles and code and you will avoid this.