Here is how to solve this:
The problem is, that a new installation come with Framework 15.0.16.27. Starting with Version 15.0.16.38 of framework, the GPG keys are updated (just have a look at the changelog and your error messages). You cannot install, because system is trying to upgrade to framework 15.0.16.42, which GPG key is not known, until 15.0.16.38 is installed. Therefore all depending modules will fail (refuse) to install.
Simply open your web interface and go to “Module Admin” in Admin Tab. Now click on “CHECK ONLINE”. After that, scroll down to “FreePBX Framework” and expand it by clicking. You will see “PREVIOUS” on the left side. Click on it. Now, you see the previous releases, with there version numbers and a “ROLLBACK” button.
Don’t be confused here, the button is named ROLLBACK, but we do an upgrade by clicking it. So, now click the ROLLBACK button for version 15.0.16.38 (DO NOT USE ANY OTHER VERSION).
The installer now will upgrade to 15.0.16.38, which WILL SUCCEED. After this, you are able to upgrade your framework to the needed version 15.0.16.42, without any problems. After that, you can install your favorite modules again.
And now, hold your applause…. your welcome 