Walkthrough

1. For completing this request, you can get Professor's Treasure Trove Habitat as a reward.
2. Help Make a Home is only accessible after completing the Do the… Team Initiation Challenge. This means you can only build Professor Tangrowth's habitat once you've reached the postgame.
3. Do the…Team Initiation Challenge Walkthrough
4. After completing the Do the… Team Initiation Challenge, talk to Professor Tangrowth in the Pokemon Center. They'll ask you to finally start building a habitat or home for them.
5. Collect 4 Large Relics for the habitat. Make sure to have them appraised first before building.
6. Build one bed for the habitat. You can choose any bed you like.
7. Head back to the cave and place all the materials around the Professor's Treasure Trove to build the habitat. | | Alternatively, the Professor's Treasure Trove can now be picked up. If you feel that Professor Tangrowth deserves a better home, you can take it and build the habitat elsewhere.

Walkthrough source: Game8.