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I've recreated an example logo:

1. Keep GaryLang, White Group and Black Stroke Group shapes in separate layers.

2. Select GaryLang layer and Object > Compound Path > Make

3. Select Black stroked Group layer and Expand it. Then use Pathfinder Unite.

4. Make this layer too a Compound Path.

5. Make sure Group layer is above GaryLang

6. Select both GaryLang and Group and use Pathfinder Minus Front.

You should get desired result.

Another way of doing this using Shape Builder tool. Once you've performed Step 3 (Compound Path not necessary for this case), select both GaryLang and Group use Shape Builder tool. There's option to remove all unwanted shapes (Alt+Click). It will *become transparent.