Few things to take into account when replacing the batteries, are the cells conneted in parallel (higher current) or in series (higher voltage)? Does your device have a regulator and reverse voltage protection? Shorting an LiSOCl will just make it warmer, shorting a LiPo cell might cause an explosion.
You said it is a wireless device, 2 1/2AA LiSOCl cells in parallel can provide a 200mA pulse, check if your intended replacement cell can provide it.
Self discharge: LiSOCl cells have low self discharge and very long shelf life. Rechargeable cells have much higher self discharge and if the cell drops below a certain threshold, it cannot be used anymore.
The in-battery protection circuitry is usually intended to act as a gross fault protector and it is strongly recommended that it not be relied on as a means of charging control. As a means of gross short circuit protection it may be suitable as long as the values they choose for max Iout are acceptable to you.
For charging, use of one of the large number of LiIon charger ICs is recommended.
A major factor is that the over voltage circuit does not remove the applied voltage when the CC charging current falls to a low value. This means that the battery is "floated" indefinitely with the risk (I'm told) of plating out metallic Lithium.
A PV panel (solar panel) that is nominally 12V rated and intended for charging lead acid batteries, will have a loaded Vout of about 18V and an O/C or light load Vout of over 20V.
The maximum voltage that you need AT the battery pack is 4.2V/cell or 12.6V in your case.
PV panel available Iout values are a reasonable approximation to being linearly related to isolation (sunlight level).
However, Vout is not related to light level in the same way. A PV panel will produce over 90% of its full power voltage for light levels of a few % of maximum and above - say at 10%+ to be safe. If you want the panel to charge the battery to fully-charged even on a low sun day, if necessary, then you need a panel that is full load rated at at least 12.6V/90% = >= 14V. As above, as an SLA targeted 12V panel makes about 18V at full-sun full-load, such a panel will provide more than enough voltage under all practical light conditions.
You will get substantially longer cycle life from a LiIon cell if you terminate discharge at a slightly higher voltage than allowable absolute maximum. With LiIon , below about 3V under medium loads you have used the large majority of the stored energy.In-battery low voltage cutoff circuitry will probably allow discharge to about 2.6V/cell, which is lower than is wise for good battery lifetime.
Best Answer
Cycle life does not mean a full charge/discharge cycle. It is the actual amount of energy that "passes through" the battery during it's lifetime. Lithium batteries have the advantage that you can also really use that high cycle life.
For example: let's say we have a battery that you discharge and charge daily and this way it lasts 1 year. ( 1 C /day => 1 year) If you were to not fully discharge this battery but discharge it until it's half full and then charge to full it would last 2 years ! (0.5 C /day => 2 years) Likewise at 1/5th discharge per day it would last 5 years.
Note how the amount of displaced energy remains the same: 1 charge per day for 1 year is the same amount of energy as 1/2 charge per day during 2 years.
This is one of the unique properties of Lithium based rechargeable cells.
Lithium cells have no memory effect, the oldfashioned Nickel-Cadmium (NiCd) cells have a memory effect, if you only use 1/2 of their capacity each day they "lose" the unused part of the capacity and they remember (the memory) that you only discharged them 1/2 last times and now they assume that's all you need.
Nickel-MetalHydride (NiMh) cells used to have high self-discharge, they discharge even when you're not using them. Nowadays we have low-self discharge NiMh cells (Sanyo Eneloop, GP ReCyKo) that have fixed this problem.
Lead-Acid batteries (used in cars mainly) are cheaper than Lithium Ion cells but can store less enery per volume.
Lithium cells have the advantage that they can store a high amount of energy in a small space and they are not very heavy.
Lithium cells must be manufactured properly though and also charged properly, mistreating them can result in smoking, fire and even explosion !