When I first plugged the battery into my laptop it read as completely discharged (even though I KNOW that the cells were shipped partially charged) possibly because the electronics had been unsoldered and lost power completely. I expect they default to a completely uncharged state if they ever loose power completely. An hour later the battery reported that it was almost halfway charged. (My laptop batteries normally take around two and a half hours to charge, getting the first 90% of the charge in two hours, and the remaining 10% a bit more slowly as the charging electronics "top up" the cells.)
At this point I went to bed, so of course I unplugged my laptop because I didn't want a newly constructed battery charging unattended. (I know what I'm doing, but it doesn't hurt to be careful…)
The next morning I plugged the laptop in and after 45 minutes it had reached 99% charged. I believe that this was because it had run up against the "last full capacity: 16880 mWh" setting that was stored by the charging electronics. It stayed at 99% charging for well over an hour, charging at a reported rate of 3109 mW with a voltage that ranged near 12.5 volts ( 12487 mV). Most Li-Ion cells reach full capacity (and regulated chargers usually stop charging) at 4.2 volts (4.2 * 3 is 12.6 volts), so it looks like the charging circuit got the cells very close to a fully charged state, even though they had more capacity than the electronics were expecting.
Once the battery hit 100 % (fully charged) I checked the /proc/acpi/battery/BAT0/info file. It reported that the "last full capacity:" was still 16860 mWh (I was hoping for something closer to 44000 mWh). The interesting thing is that the battery used to report a "design capacity: 44000 mWh", but now it reports "design capacity: 47520 mWh" which is an improvement in the correct direction.
I ran the battery completely down (which took 2 hours and six minutes) by using the laptop normally (but with full screen brightness) for an hour, and then running a script to use 100% of the CPU for the next hour and six minutes. This is about the same battery life I would expect for a brand new 4.4AH battery (I expect 2.5 hours of power when not running the CPU and back-light at 100%) so it looks like the cell transplant was successful.
However, the power monitoring electronics in the battery took a while to get used to the new cells. On the first discharge the ACPI based battery gauge dropped rapidly in the first 45 minutes, and then stuck at 6% remaining for the next hour and ten minutes. However, the laptop BIOS (which controls the color of the power LED) had a better idea about how much life I had left, as the green power led didn't turn orange and start flashing until near the 1 & 1/2 hour mark. Near the end of the discharge period I noticed that the reported "last full capacity" had raised to 20230 mWh.
Over the next several discharge/charge cycles the "last full capacity" slowly raised in approximately 4000mWH increments.
original: 16860 mWH
1st: 20230 mWH
2nd: 24220 mWH
3rd: 29040 mWH
4th: 34750 mWh
5th: 41660 mWh
It appears that the electronics are unwilling to raise their view of the cell's capacity by more than 10% of the design capacity per cycle. The battery has now stabilized with a reported capacity just over 4.1 AH. This is 0.3 AH less than the new capacity of the Li-Ion cells, but it's what I would expect as the charge/discharge electronics are slightly conservative and you can get a few extra minutes of power out of the battery after it reaches "0%".
Knowing what I do now, I could repeat the entire procedure in 2 to 3 hours, so the $7 savings over buying a $50 4.4AH "compatible" battery isn't really justified. However, if you spent $65 for the 2600 mAH cells, you could have a battery that has 8% more capacity than the $100 to $120 official IBM/Lenovo 4.8 AH battery packs (and 15% more capacity, or 22 extra minutes, than my $43 battery) with the same amount of work.
18 month update: Current battery status.
Some charge control circuits will “shut down” if the existing cells are removed (similar to inkjet cartridges that refuse to be re-filled) so you may want to solder your new cells into a pack, connect it to your circuit in parallel with the old cells, and only then cut off the old cells. Think of this as Indian Jones sliding the statue off the pedestal while at the same time replacing it with a bag of sand…hopefully with better results.
The charge control circuit in my (after-market) X31 battery did not have this problem, and didn’t mind not having cells attached for an hour or two (it started right back up), but others have reported that some battery charge circuits will detect a complete removal of cells and stop functioning.