It will outlast you. Within reason.

Jerusalem stone is porous, unsealed, and three thousand years into proving it can cope. There's very little to do — but there are two or three things worth not doing.

Everyday

A dry soft brush, or a barely damp cloth. That's genuinely it. Dust sits in the carved channels and a brush lifts it out better than any cloth will.

Marks and stains

Oil from hands is the usual culprit and it fades on its own. For something stubborn, a paste of bicarbonate of soda and water left on for an hour will draw most of it out. Anything worse, email a photograph before you try anything.

Outdoors

Perfectly fine, and where a lot of these end up. Expect the surface to soften and the colour to deepen over years — that's the stone behaving correctly, not failing. Pieces on the Old City walls have been doing it for millennia.

If you'd rather it stayed close to how it arrived, keep it under an eave and apply a breathable stone wax once a year. Use a wax, not a sealer: a film-forming sealer traps moisture behind it and does more damage than weather ever would.

Freezing climates

Water in the pores expands when it freezes. In a hard-frost climate, either mount it somewhere sheltered or wax it before winter.

The scroll

The klaf inside is parchment and cares far more about the weather than the stone does. Tradition is to have it checked by a sofer twice in seven years; if the case lives outdoors, err toward the shorter interval.

Chips

A chipped edge on a hand-made piece is not a failure, and Avraham would rather you left it. If it bothers you, send a photograph and he'll advise.