How can I edit the string "Send this user a private message" in Privatemsg Is it possible in the Privatemsg module (7.x-1.3) to edit the string "Send this user a private message" to something else without directly editing the modules code?
Have you tried String Overrides module? Here is a quote about it (from the module's project page):

... a quick and easy way to replace any text on the site.
Features:

Easily replace anything that's passed through t()
Locale support, allowing you to override strings in any language
Ability to import/export *.po files, for easy migration from the Locale module
Note that this is not a replacement to Locale as having thousands of overrides can cause more pain then benefit. Use this only if you need a few easy text changes.