Yes. Configure Jenkins nodes and name them, say master and slave (Manage Jenkins → Manage nodes).
1) Set up Job A and indicate that it can only work on master ("Restrict where this project can be run" and put master in the label field).
2) Configure Job B so that it only works if Job A succeeds:
"Actions after assembly" → "Trigger only if the assembly is successful"
3) Pin Job B to slave as in step 1.
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