Heroes have bows only when they are of the same civ they are owned by. Julius will still have artillery barrage no matter what civ he belongs to, as well as Cleo's converting power, Achilles invulnerability, Ramses rejuvenation, and Germanicus's scare away power. Not so for Alexander's fire bow, or Sargon's multi-arrow bow.
If you want a cross over power, try using replace effect to change heroes.
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