You summed it up very well here. It's vice versa too. So I must say that protect your account on the other forum too so that anything bad does not affect you on this forum too.
Do you mean it's better if we teleport the account there? Instead of having our account cloned or having the username imitated in another forum? This sounds logical to me and perhaps regardless of whether we want to use that account or not, at least no one can claim our account on another forum.