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Your first approach is not correct, because by adding the LinkButton as target control for the RadToolTipManager, you simply try to tooltipify that LinkButton. As a result, when you click the button, the manager tries to open another RadToolTip for this LinkButton. However, you cannot have two RadToolTips open at the same time and that is why the second tooltip does not open.
Regarding your second approach - this approach is correct and the result you describe is expected. As you add the control to the RadToolTip dynamically, the RadToolTip should recreate this control on postback. Otherwise, after you click the LinkButton in the TestThree.ascx control, the RadToolTip will be empty. That applies to all dynamically added controls to the page - you yourself must make sure that you recreate those controls when their part of the page is updated.
In case you still have problems with that, I would recommend that you first implement the behavior with a standard UpdatePanel control instead of a RadToolTip and then apply the same approach for the RadToolTip. In case you have problems with this, just send us your solution with an UpdatePanel and we will help you implement it with a RadToolTipManager.
the Telerik team