As another user said, not true.

Not entirely true, anyway. There are factors like which node is being used to broadcast the transaction, and other network related factors which debunk that this strategy in any way helps your anonymity.

However, what it does do (if you do it with more sophistication than just moving it between your own wallet) is that it can potentially increase the ambiguity of whether or not the coins are still yours, or if they are now someone else's.

We are aiming to add a Cybersecurity & Privacy board to the forum, where we can discuss topics like this from the perspective of privacy. If that interests you, support the poll and write why you want the board added