I don't think you'll be able to strip it off, so sand lightly, patch any defects, and apply a similar stain. I use Dulux Woodsheen but there are various brands. Ensure the owner is paying for materials. Stir very thoroughly. Start with a smallish tin and see how far it goes. If you assume one tin for a door, you will probably need at least 5 litres for a shed, a couple of coats.
there is a faint chance you will find an old tin in the shed.
Any rotten bits (likely to be near the ground) pull off and replace with new shiplap, giving it multiple coats of wood preserver after cutting and drilling it, but before fixing it.
A tip to match the colour (it looks like dark mahogany stain to me, which is very red. Walnut is brown. ) is to use wood dye on any patched or new areas. Wilko have a surprisingly good range at low price, but Blackfriars or Rustins is good. Avoid the new water-based "refined" Colron, which is rubbish. Spirit-based Colron, if you can get it, is fine. You can apply the dye with a soft brush on rough work, but lightly, and rub off excess with a rag after a few minutes. You can mix them to match a colour.
If you have the base colour correct and even, you do not need to use a coloured stain when recoating (it will make the result darker).
It is much easier to put in new shiplap than to try to bodge and repair old pieces. The bottom edge overlaps the one beneath, so lever that away, then try to pull it downwards. The nails are probably rusted.