Hi! It's difficult to see how extensive the damage is! I often use a "Feiner," a saw multitool machine that can cut/saw at all sorts of seemingly impossible angles. You can cut out a piece horizontally at an angle upwards: confused: sounded strange when I read it myself. Hmm! Yes, cut away the damaged material, as straight as possible but not straight in, instead at an angle. Insert a new piece at the same angle so that moisture cannot get into the joints. But it works perfectly well to do as you intend, if I understood you correctly! Regards, "full-time builder"
Hello
If you imagine the joint where the timber ends meet, the moisture damage goes about 80-90 cm "backwards" along the long wall and probably through the entire log (that is, into the house).
My idea was to cut where the timbers meet, replace the damaged piece, and then take care of the joint itself, which is also moisture damaged at the bottom. The timber that goes away on the gable wall seems undamaged.
Can you put some form of sealing in the seam that will be created?
If you imagine the joint where the timber ends meet, the moisture damage goes about 80-90 cm "backwards" along the long wall and probably through the entire log (that is, into the house).
My idea was to cut where the timbers meet, replace the damaged piece, and then take care of the joint itself, which is also moisture damaged at the bottom. The timber that goes away on the gable wall seems undamaged.
Can you put some form of sealing in the seam that will be created?
It is possible to seal, but the best is to insert a "wedge" that is oiled. Is the timber treated with iron vitriol? Or painted? The best for timber is oil... otherwise, there are many new materials to use, you should ideally ask the paint store about that. But my advice is to chisel/saw away damaged wood, it can be difficult to fit in new pieces if you don't have access to good tools 
I have almost everything the market can offer myself, so it feels a bit wrong to give advice on "how" to do it...
I have almost everything the market can offer myself, so it feels a bit wrong to give advice on "how" to do it...Can you access the timber from underneath? If you can, it might be easier to completely cut off the bad pieces like cutting a log, but from underneath with, for example, a reciprocating saw with a long blade. Cut everything bad, e.g., 1 meter in both directions and at the corner. Attach reinforcements on the inside from underneath, fit in a new corner. Drill through and screw it fast from the outside and through the timber so it is really secure. If done correctly, it is almost unnoticeable that it has been repaired. I have owned an 18th-century timber farm and am a carpenter, so I find it enjoyable to restore older buildings.
Note! I forgot to mention that you should preferably leave everything as is unless it's completely rotten; too many people replace timber unnecessarily. It might be enough just to oil the lower part that is bad without needing to make a bigger deal out of it! If you use red paint on the timber, it becomes more difficult to make it look nice without replacing bad parts; painting is unfortunately required on at least the affected sides, but feel free to paint the whole thing. If the building is on stone, it may have shifted over the years, causing water to get into the timber from below. It might be worth checking with a sheet metal worker if they can make a nice metal edge around the facade at the bottom. It doesn't cost many hundreds...
Thanks for all the advice and tips.
I can't access it from underneath.
Since we live in the house (which is to be sold), I can't access it from the inside without tearing down the inner wall in the kitchen, and there's neither time nor desire for that right now, so I can't install studs from the inside.
The timber doesn't seem to be treated with anything at all.
It's a pity you live so far away, it would have been interesting to meet in person to see what you mean.
I can't access it from underneath.
Since we live in the house (which is to be sold), I can't access it from the inside without tearing down the inner wall in the kitchen, and there's neither time nor desire for that right now, so I can't install studs from the inside.
The timber doesn't seem to be treated with anything at all.
It's a pity you live so far away, it would have been interesting to meet in person to see what you mean.