I have a WAR file with the following structure:

The JSF managed bean <
You need to have a JSF 2.0 compliant /META-INF/faces-config.xml file in the commons-web-1.0.jar file in order to get JSF to scan the JAR file for classes with JSF annotations like @ManagedBean and auto-register them.
JSF does namely not scan every class of every single JAR file in the classpath, that would have been too expensive. Only JARs with the above /META-INF/faces-config.xml file will be scanned.
You should also ensure that you do not have the metadata-complete="true" attribute in the declaration of webapp's own /WEB-INF/faces-config.xml file, otherwise JSF will assume that this faces config is complete and therefore won't auto-scan JAR files for annotations.
If none of those conditions are (or can be) met, then you need to manually register the bean as in webapp's own /WEB-INF/faces-config.xml instead of relying on annotations.
See also chapter 11.4.2 of JSF 2.0 specification (emphasis mine).
11.4.2 Application Startup Behavior
...
This algorithm provides considerable flexibility for developers that are assembling the components of a JSF-based web application. For example, an application might include one or more custom UIComponent implementations, along with associated Renderers, so it can declare them in an application resource named “/WEB-INF/faces-config.xml” with no need to programmatically register them with Application instance. In addition, the application might choose to include a component library (packaged as a JAR file) that includes a “META-INF/faces-config.xml” resource. The existence of this resource causes components, renderers, and other JSF implementation classes that are stored in this library JAR file to be automatically registered, with no action required by the application.