Quite correct.
Everyone that is baptized and repents and believes that Christ is Lord, receives the HS.
Paul himself states that no man can proclaim and believe that Christ is Lord ( and all that goes with that proclamation and belief) unless He has the HS.
Now, does that mean that ALL that are baptizzed or all that proclaim HAVE the HS?
Personally I don't think so BUT it is not for any believer to judge another in that way.
Leave that one up to Father and Son.
Can one that has the HS "lose" it?
Yes, and no.
They can deny the HS, yes and I guess that can be viewed as losing, but it is more like blaspheming against the HS.
I don't think that many that have the HS deny Him, I think that many proclaim to have it ot proclaim Christ because they are "born in" or because they believe they are expected to or because they believe that in doing so, they are somehow "special" or "unique" and then, when they realize that is not the case, they "lose their faith". Sometimes their faith is tested ( by themselves) and they come up wanting.