[ACCEPTED]-How to run a Jenkins build only if another build has been successful?-jenkins
Try BuildResultTrigger Plugin - you can set it in job B to poll the 1 results of job A with the desired (un)frequency.
I would recommend the Parameterized Trigger Plugin. As a post-build 3 step on B, have job A be triggered on a 2 successful build. You don't have to specify 1 parameters.
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