✓

Yes - show her the artifact. It's the safest path into Last Light Inn: instant trust, no skill checks, and the artefact can't actually be taken from you. The item is magically bound to its owner, so "handing it over" for inspection never leaves your inventory.

What each option does

As long as you don't attack the Harpers, every non-violent path gets you inside - the artifact just skips the dice rolls.

ChoiceOutcome
Show the Mysterious ArtefactImmediate trust, zero checks - Jaheira lowers her guard and invites you in. The artefact stays in your inventory.
Charisma check (DC 21)Talk your way out of showing it - pass and you're in; fail and things get tense.
Strength check (DC 15)Break out of the Entangle - same result, you get in either way.
A companion vouches for youLassandra, Mol or Marcus can intervene on your behalf if they're present - free pass.
Attack the HarpersDon't - you're facing about ten of them, and it poisons the entire Act 2 safe zone.

Why showing it is safe

The two fears players have - losing the item, or Jaheira turning hostile over it - are both unfounded.

FearReality
"She'll take the artefact"Can't happen. It's a Bound story item - bound items can't be removed from your inventory by any NPC.
"She'll think we're with the Absolute"The opposite - the artefact proves you're a True Soul who kept your autonomy, which is exactly what she needs to see.
"It locks me out of options"No downside recorded - you get the same inn access, same vendors and quests, minus the skill checks.

The scene right after: the wine

Once inside, Jaheira offers you a drink. A DC 10 Medicine check reveals it's spiked with a truth serum - but the choice matters less than it looks.

ChoiceOutcome
Drink itWhen she asks if the parasite is changing you, lying requires a DC 6 Constitution check. Most companions disapprove of drinking.
RefuseYou keep the option to simply lie to her question. Most companions approve.

Either way she sends you upstairs to Isobel - heal up first, because that conversation kicks off a fight.

FAQ

Does Jaheira take the artefact if I show it?

No - the Mysterious Artefact is Bound to its owner and can't leave your inventory. Showing it is inspection only.

What happens if I refuse to show it?

You pick another route in - a DC 21 Charisma check, a DC 15 Strength check to break her Entangle, or a companion vouching for you. All lead inside.

Can Jaheira become a companion?

Yes, later - gaining her trust at Last Light Inn is the start of that path. Keep the Harpers alive through Act 2.

Does showing the artefact affect Shadowheart?

No lasting effect - it's her item mechanically, but the scene plays the same and the artefact remains bound.