My recommendation would be to bolt the new framing lumber that is a wide as the existing beam so that it rests on the existing plate and use 6' material. Make sure the new materials are able to have a surface on the existing beam that is solid enough to bolt thru. I recommend using Fasten Ledgerlok. You can get them from Home depot .

Is there a reason you don't want to do the whole 12 feet? It looks like it's currently open to the outside, so getting that length into the basement shouldn't be hard.

Seems like the easiest and best option to me.

If you can get the whole length in even better. I was not sure if the access would allow it.

If one must ask how a job like this should be done,it's best they hire a pro. The beam look's like it might be rough hewn Bois-D-Arc. If that's true,there's no need for replacement,it will last another 100 years. If rot go's all the way through,I'm not sure new material should be in contact with rot. Unless floor can be jacked up and held during repair, I would consider A. Installing another beam parallel and a few inches to the side. B Using 1/2" narrower laminated beam to ease getting into position and C. Shimming 1/2" between beam and plate.

Thanks for all the tips. Finished the job today. For anyone else who may need to do this, this is how I did it. I cut off the rotted part and cleaned off the old board with tor-bor and let it dry. I used an 8x14 (cut to size) and sistered it to the old board with 8 x 1/2" bolts, construction adhesive and nails. Key was to jack up the new board at the end nearest the center beam so it would fit tight against the sub floor and even with the old joist.

I would have preferred to run the new joist across the center beam but getting it on the beam was too much work as it was not an easy fit.