Last but not least the question; how to charge the lead gel battery? For a 12Volt drill you can use the usual charger. For drills with a higher voltage you have to use an adaptor with a 12V till 14 V unstabilized DC output. Its easy to connect the adaptor cable to the charger because there is no electronics build in.

Addition: To avoid wasting the old adaptor, you can use a charger IC. It is the PB137. You need only 2 capacitors extra. See the diagram. The input voltage can be between 16 and 40 Volt DC. This circuit fit's easy within the charger unit.