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Hello again and I apologize for the delay in getting back to you but I was out of my office for a bit. No, unfortunately, a General under Honorable Conditions is not sufficient to qualify for your post 9/11 GI Bill. You would have to have an Honorable Discharge. If you have been in long enough to have previously received an Honorable Discharge after completing a full enlistment, that discharge could be used instead of the current one.
I hope this answers your question.