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We are all prisoners inside the cage of our own flesh.
1) The Player receives the Profit immediately after this Card's Incorporation or only during Production Phase ?
Yes, you also receive the profit immediately after incorporating this Location, just like with other Production Locations.
2) The Profit is duplicated or is it a theft (the other player don't gain the production) ?
It's not a theft.
Winter manual, p.10, Suppliers description wrote:
If you want to receive Profits from a Location for which production depends on some conditions fulfillment, like in the case of previously mentioned Engineers’ Guild, first check whether the player who owns this Location meets the production requirements. Thus, if the Engineers’ Guild can provide him with 2 VPs (as he has 3 Scrap type Locations), you also receive 2 VPs when using Suppliers on the Engineers’ Guild Location.