Charging cell phone batteries in series

[najrao]

I am using 7 'tablet' batteries in series to power a dc motor. Each cell is 4Ah, 3.7V Li ion, genuine Samsung, with its own BMS. I have made up a mosfet current limiter, to 2.5A, just for the moments the motor starts up (milliseconds, but 20 times a day). There is no balancing, but I have checked each cell initially to be 4.12V +/- 20mV, after full charge. Also, a simple indicator shows if the total voltage dips below some 22.5V, especially during the motor start,  for me to charge again.
I can only charge by a CC/CV bench psu, set to 1.0A, 29.4V; I may choose 2A later.
If and when one of the cells cuts off, having reached just over 4.2V, all cells get cut off too. My surmise is that this is still safe, and the one BMS mosfet turning off will not see any severe overvoltage. Would I be right in this?

[sleemanj]

Yes as long as the cells all have protection (under voltage, over voltage and over discharge current is typical) than that should be fine, once one trips out they all will, charge them up fully to start with individually before you series them up so you have the maximum life possible (that of the smallest/worst cell).