Start with the heart. Tight mitral stenosis stretches the left atrium, and once atrial fibrillation sets in the atrium no longer empties properly. Blood pools, thrombus forms, and a fragment can shoot off into the cerebral circulation. That embolus lodges in an artery and starves a region of brain of oxygen.
Now weigh the timeline against the formal definitions. A transient ischemic attack is strictly time limited: the deficit must clear inside 24 hours with no tissue death. Here the arm weakness lasted a full two weeks. That alone rules a TIA out, because tissue infarction must have taken place for a deficit to last that long.
Persistence beyond a day is the textbook line that defines a completed stroke. The later return of strength simply reflects the brain's capacity to recover function around an infarct; it does not downgrade the event to a TIA.
Choosing the subtype is straightforward once the mechanism is clear. An embolus blocking flow produces an $ischemic$ infarct, not a bleed, so hemorrhagic stroke is wrong. Vasculitis is an inflammatory arteritis unrelated to a clear cardioembolic source like mitral stenosis with AF.
\[\boxed{\text{Ischemic stroke}}\]