Test Suite A and Test Suite B are supposed to be independent each other. This is how Test Suite concept is designed
This implies, your Test Suite B depends on the the previous Test Suite A. Then I think you should not group your test cases as test suites. I would rather recommend you to use “Controller TestCase pattern” implemented using WebUI.callTestCases() keyword. See the following post:
Test Suite - Script Mode - set up method - how to pass common data value - #5 by kazurayam