When you posted your question, the site polled your plugins and found Flash version 22 instead of the current version 23. There might have been a problem updating the files (if Flash was in use, for example), or Firefox might not be updating its list of installed plugins. To investigate further:

Check for the Physical Presence of the Plugin DLL

On 64-bit Windows 7 that is here:

C:\Windows\SysWOW64\Macromed\Flash

and the file would be named NPSWF32_23_0_0_185.dll (unless there is a newer version with something different instead of 185).

If you do not have that file but instead have an older version: Re-run the Flash 23 installer, making sure that Firefox is not using the old plugin.

If the file is there... and exiting and starting Firefox back up does not discover it...

One possible reason for an installed plugin not to appear on the Add-ons page is if Firefox has been set NOT to scan the registry for plugins. Another is that Firefox's settings file storing plugin data has become corrupted. Here are the steps to check those possibilities:

Confirm that Firefox is scanning the registry for plugins

Firefox finds the Flash plugin from a registry entry. Some users have the scanning turned off for some reason. Here's how to check and fix that:

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the filter box, type or paste scan and pause while the list is filtered

(3) If plugin.scan.plid.all is not set to its default value of true, double-click it to toggle it back to the default.

If you changed this setting, exit and restart Firefox to trigger another scan.

If you check the Add-ons page, Plugins section again, can you find "Shockwave Flash" there with the current version number?

If Firefox is set to scan but still does not find Flash and list it on the Add-ons page...

Remove Firefox's plugin registry file

Sometimes the pluginreg.dat file becomes corrupted. You can remove it and have Firefox re-scan for plugins.

Open your current Firefox settings (AKA Firefox profile) folder using either

• "3-bar" menu button > "?" button > Troubleshooting Information
• Help menu > Troubleshooting Information
• type or paste about:support in the address bar and press Enter

In the first table on the page, click the "Show Folder" button to launch a new Windows Explorer window showing your settings files.

Leaving that window open, switch back to Firefox and Exit, either:

• "3-bar" menu button > "power" button
• File menu > Exit

Pause while Firefox finishes its cleanup, then rename pluginreg.dat to something like pluginreg.old

Start Firefox back up again. (If you want to restore your previous non-private session, use History > Restore Previous Session.)

When you return to the Add-ons page, is "Shockwave Flash" finally there?

The vast majority of Flash Player versions since December 2014 has been affected by critical vulnerabilities as to why the previous versions can be set to click to play soft blocking sometime after recent Flash update.

If the security concerns of the Flash Player versions were minor then they likely would not be put on blocklist like was the case back during March t2013 to December 2014.

Mozilla does not block Plugins because they hate them or for being old.

https://addons.mozilla.org/firefox/blocked/.