Getting "WELD-001408 Unsatisfied dependencies" error when injecting a bean from a JAR in WAR

Issue

• In a WAR application (myapp.war) we try to use an injected bean class which is defined in another JAR (another-bean.jar). The WAR application looks like the following:

myapp.war/
└── WEB-INF/
    ├── beans.xml
    ├── classes/
    │   └── ...
    ├── lib/
    │   ├── another-bean.jar
    │   └── ...
    └── ...

• But this gives us the following error. Why doesn't it work?

09:57:08,291 ERROR [org.jboss.msc.service.fail] (MSC service thread 1-11) MSC000001: Failed to start service jboss.deployment.unit."myapp.war".WeldStartService: org.jboss.msc.service.StartException in service jboss.deployment.unit."myapp.war".WeldStartService: Failed to start service
    at org.jboss.msc.service.ServiceControllerImpl$StartTask.run(ServiceControllerImpl.java:1767) [jboss-msc-1.0.4.GA-redhat-1.jar:1.0.4.GA-redhat-1]
    at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145) [rt.jar:1.7.0_51]
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615) [rt.jar:1.7.0_51]
    at java.lang.Thread.run(Thread.java:744) [rt.jar:1.7.0_51]
Caused by: org.jboss.weld.exceptions.DeploymentException: WELD-001408 Unsatisfied dependencies for type [AnotherBean] with qualifiers [@Default] at injection point [[field] @Inject private com.example.myapp.MyServiceImpl.anotherBean]
    at org.jboss.weld.bootstrap.Validator.validateInjectionPoint(Validator.java:311)
    at org.jboss.weld.bootstrap.Validator.validateInjectionPoint(Validator.java:280)
    at org.jboss.weld.bootstrap.Validator.validateBean(Validator.java:143)
    at org.jboss.weld.bootstrap.Validator.validateRIBean(Validator.java:163)
    at org.jboss.weld.bootstrap.Validator.validateBeans(Validator.java:382)
    at org.jboss.weld.bootstrap.Validator.validateDeployment(Validator.java:367)
    at org.jboss.weld.bootstrap.WeldBootstrap.validateBeans(WeldBootstrap.java:379)
    at org.jboss.as.weld.WeldStartService.start(WeldStartService.java:64)
    at org.jboss.msc.service.ServiceControllerImpl$StartTask.startService(ServiceControllerImpl.java:1811) [jboss-msc-1.0.4.GA-redhat-1.jar:1.0.4.GA-redhat-1]
    at org.jboss.msc.service.ServiceControllerImpl$StartTask.run(ServiceControllerImpl.java:1746) [jboss-msc-1.0.4.GA-redhat-1.jar:1.0.4.GA-redhat-1]
    ... 3 more