Charging 18650 Lithium Ion Cell With 12.66V Solar Panel & BMS Board—Charge Time?

I connected a battery managementSystem board to a solar panel. ThenI connected 1 lithium ion cell to Battery management board. According to the datasheet for the bms board theCharging voltage is between 12.6 voltAnd 13 volt. The measured the voltageProduced by the solar panel. It is usually12.66 volts or a little more.  I measuredThe voltage at the output of the bms Board it is 12.66 volts or a little more.Is it true that if the 18650 lithium ionCell is at 4 volts this means the cell isFully charged.   How long will it take toRecharge 18650 lithium ion cell at 12.66Volts. This within the stated rechargingVoltage. How long do 18650 lithium ion cells Take to recharge. Any way to tell ifIt is fully recharged.

OK, David, for starters it sounds like you need to know more about 18650 Batteries.  Here is a good introductory article.  Here is a table taken from it:
The point at which most Li-ion batteries are reckoned to be fully charged is 4.2V and this is important, it is listed under Charge Method in the table..  If you exceed this you're likely to start a fire.  This is what you have a Battery Management system for.  The charge method is given as CC-CV - Constant Current, Constant Voltage.  The battery is charged at a constant current until it gets to 4.2 Volts and then charging is terminated.  The standard charge current is given as 1.25A -- this will charge the battery in 3 hours max, but you can go as high as 4A which will do it in less than 1 hour.  For maximum battery life I'd stick to the standard rate or less.In addition, it's best not to discharge these batteries too much either, the link above gives 2.5V as the cutoff voltage - if you discharge it more than this you may permanently damage the battery.  I wouldn't even go that far.The maximum current you can draw form these batteries is 20A and this will vary from battery to battery, it is always worth looking at the specifications if you are going to go anywhere near that.You say "The voltage at the output of the BMS  Board it is 12.66 volts or a little more."  I presume that is open circuit, ie with no battery connected.  But you also say "According to the datasheet for the bms board the Charging voltage is between 12.6 volt And 13 volt".  I suspect that this board is designed for 12V lead acid batteries.  If this is the case it is the wrong board for your 18650 battery and will overcharge it, so STOP USING THIS BOARD!  you may start a fire or get and exploding battery
What is important is what it does with the battery when connected,  It should stick to all the limitations above, especially the maximum charge voltage.  You give very few details about the BMS Board you are using, if you can post a link to it I could comment on that as well.  I would hope it is specifically designed for these batteries, or at least for Li-ion batteries.  If not you risk damaging your battery, or worse, these batteries do not like mistreatment.  Please check this, it is important.

I think the advertisements said it isFor lithium ion batteries. I am a beginner. I know very little aboutSolar panels and lithium ion batteriesAnd his boards. The model of bms Board is hx-3s-25a I think. To lookUp specs I just type hx-3s-25a. Sorry IAm very new to all this. The lithium ionCell was at 3.7 volts then it increasedTo 3.73 volts. That means it is workingRight.

how it will have cost?

David that board is for 3 x 18650 batteries or even banks of them - see this site.  It has pics of the board used with banks of 3 x 18650 batteries.  Now whether it will charge one cell only it does not say - I would say not but the specifications given do not say..  These boards are set up to charge three batteries and make sure none of them get over 4.2V.You can get boards that will charge one cell only like this one from Adafruit.  However they usually need USB Power (5V) or a lower voltage like 6V in this case, not your 12V solar power.
If your solar power is set at 12V you could get a switching regulator to bring it down to 5V without losing efficiency, something like this also from Adafruit. 6-32V input to a 5V 1A output.You may be able to find a board that can take up to 12V or more input and charge one 18650 battery, it would have a switching type regulator built in I think.  I could not easily find any on a quick search.Edit - David to see if your board will cope with a single battery only, put your solar panel on the power input and the battery between B- (-) and B1 (+) and see what the voltage does.  As above it should go up to  a maximum of 4.2.  If it gets any higher than this, you need a different board.  If it does not get anywhere near 4.2, it is not charging properly and you still need another board.

Could I use a smaller voltage to rechargeThe batteries? For example 9 volts or6 volts.

David Yes, very much so, for charging a single 18650 battery, 5V is sufficient.  But I would suggest you get a different board, intended for one Li-Ion battery only,  like this one from Adafruit that I mentioned above.  It can use USB Power (5V) or a voltage up to 6V (so you could use a 6V solar panel for this).  This would be your best solution if you are able to use a 6V solar panel.  The board regulates the charge to the battery, and has to drop the voltage form the input, which dissipates heat, so a board like this would overheat if you put too high a voltage on the input, you need to stick to 6V maximum.I'm sorry about the delay in replies, I am in Australia so it's the time difference....

One of them had a voltage of 3.72 volts.Now I can't get a voltage reading fromThat same 18650 lithium ion cell. DoesThat mean it is fully discharged?

David even a fully discharged cell should give some voltage on a multimeter - maybe less than a volt but I would expect at least a few hundred millivolts (ie a few tenths of a volt) or more.Are you measuring right on the battery terminals?

Recently, it has become fashionable to use lithium power sources for both LED flashlights and photo-video devices. All is well, but lithium cells need careful handling. Charge them carefully - up to a voltage of 4.2 volts, also discharge to a certain voltage, because if you deviate from the standards, you can irreversibly damage the battery or even start a fire.In fact, it is not so difficult to make self-made solar charging, it is enough to stock up on all the necessary components and have some soldering skills. The main elements of the future charging battery are photocells. They determine the power and performance of the device, its output current, and voltage. See here