Depending on your materials and tools, solder or weld the new batteries to the battery terminals

Depending on how badly damaged have the old metal strips become when ripping off the welding from the batteries, you might be able to reuse them and just solder/weld them to the new batteries. However, in most cases you'll have to first unsolder the old strips from the circuit board.

Soldering to battery terminals is perhaps the most difficult part of this entire procedure. Here's a pretty good Youtube video that shows how to do it.

When connecting the batteries, remember that the wiring needs to be passed through the two halves of the battery assembly. Once the batteries are soldered to the circuit board, you won't be able to re-assemble the battery housing around it any more.

In the photos are shown the three circuit board locations where the batteries need to be connected to

B+ and B-

The batteries need to be connected between themselves, making a series of 2 batteries

The mid-point between the batteries needs to be connected to the terminal at the bottom end of the circuit board (2nd photo). NB: it is necessary to connect this point too, otherwise the vacuum will refuse to charge the batteries