in Pokemon heart gold the team rocket HQ is in mahogany town the souvenir shop. you have to fight the red gyrados and then lance will appear. then go into the souvenir shop and the golden box thing will be moved by lance and you can go down there into the HQ.
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Team Rocket's hideout is in Mahogany town. Team rocket can be found in the radio tower and in the underground basement in Goldenrod after you beat Pryce of Mahogany town (who cannot be fought until you take down team rocket in the same town), but they have no "hideout" in Goldenrod.
You can find the TM Thief in the Team Rocket hideout in Mahogany Town.
there is no hideout in kanto because in pokemon red you beat team rocket and in this generation team rocket left kanto and went to johto you run into a team rocket member that stole the machine part from the power plant that doesn't mean that team rocket returned to kanto
It allows you to use the elevator in the Rocket Hideout, which allows you to reach Giovanni at the end of the hideout.
Lance gives you HM 7 Whirlpool in Mahogany town. Once you help him shut down the generators in the Team Rocket hideout, he will give you Whirlpool.