No, you may not as you came with the intention for Hajj or Umrah. This means that you have to make your intention when you pass by the Miqat.

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They can pick it up from wherever they want but it is not part of the Sunnah to pick it up from Mozdalifah

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It is OK to wear the clothes from his home but it is not Sunnah to make the intention for the Umrah from his home he should do it just before reaching the Miqat. If he had already did it from his home, there is no need to repeat it.

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