Is it possible to intgrate a function to my program (that can controll and checks the smartlocks) to automatically send invites for specific nuki smartlocks out of many?
I can’t find anything to do so
I am not 100% sure what you are looking for.
I try some general infos to see if it helps you: 
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You can create invites for a user to a pecific group of Smart Locks via the Web API with https://api.nuki.io/#!/SmartlockAuth/put by providing an array of Smart Lock IDs.
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The invite code (one code for the whole Smart Lock group) ist sent out by us via E-Mail (that’s why you have to add a user with e-mail first to whom you assign the authentication as mentioned in 1.)