If a card is a copy of The Foretold Soldier on the battlefield, it can be exiled by the triggered ability and will become foretold. However, it may only be cast this way if it has a foretell cost in exile.

Because exiling a card with foretell from your hand is a special action, you can do so any time you have priority during your turn, including in response to spells and abilities. Once you announce you're taking the action, no other player can respond by trying to remove the card from your hand.

Regardless of who controlled The Foretold Soldier and exiled it with its triggered ability, only its owner may cast it from exile this way.

Casting a foretold card from exile follows the timing rules for that card. If you foretell an instant card, you can cast it as soon as the next player's turn. In most cases, if you foretell a card that isn't an instant (like The Foretold Soldier), you'll have to wait until your next turn to cast it.