Not gonna lie, I've heard of driving LEDs with FETs, but I don't have the faintest idea on how to do so. Didn't put enough points into electronics the l;ast time I leveled up.
You need more than this, but there are youtube tutorials and other online resources/diagrams. Here's a quick primer that should explain why this is the right way to go about it.
A Fet is a kind of transistor. In fact, ordinary (non Fet) transistors could be used for this, but Fets are much more forgiving in all ways. Also larger, but that's changing.
The names vary, but all transistors have 3 legs. One of these called the Base, or Gate, is for receiving a small signal which acts as a switch. That's all a transistor is: a switch, but instead of pressing it manually, you use a small voltage. You can imagine, this can be very fast and is very useful.
The other 2 legs are basically positive and negative in a circuit using much higher voltages or currents.
Note, your small positive voltage applied to the Gate flows out through the same negative, as the other, larger voltage circuit.
So the idea would be that you connect your LED string up with the Fet in series, usually on the common positive of the LED string, and the appropriate battery power supply for the string.
You then connect the Base/Gate to your much smaller voltage signal that the economy board produces.
Hence, the small voltage signal switches the Fet to its ON state, and the high-voltage circuit is switched on.
Thus, when the econo-board tries to light an LED or small string that it used-to, the result is your much larger and more powerful string is switched on instead.
There are different transistors and fets for different situations, but the most approachable and most likely to be what you need, is an N-channel Mosfet. I hope that helps and wasn't too patronizing.