I added a wet kit to our tractor for the exact reason that you describe.
I cannot be definitive about pto compatibility between transmissions, but I believe that most, if not all Eaton trans will accept the same pto. It sounds as if you will need to purchase that part anyway, so as long as you get one that will work for your trans you should be good. I believe that the rotation can be changed in the pto, as well as gearing, but where you will be purchasing this just find out the model number of your friends pto, and buy one similar.
You will need to know if your friend's pump is married to his pto, or separated and driven by a drive line as well.
Because your friend has used his on a live bottom trailer, the pump will have been set up for a two line system, which is what you will need. Most pumps can be plumbed either for two line, or single (for use with end dumps). The difference is primarily whether or not the fluid returns to the tank back through the pump, or returns to the tank via a separate return line, circulating all the time. You will need to get a diagram of how the hoses need to be plumbed, or just take a close look and notes of how your friends is plumbed, assuming his new pump and the one that he is giving you are plumbed the same.
Your friend will have either had a hydraulic oil tank/cooler (often used on systems like crude oil tankers) or a large hydraulic reservoir - 35 to 50 gallons. On ours, we put on a large hydraulic tank so that we could also pull a semi end dump, and have enough oil capacity to fill the end dump ram. In order to do this, we installed the valveing in the cab such as needed for the end dump, and when we use it for our lowboy we just have to put the valve in the lift position. This will allow fluid to cycle through your lowboy valveing and return to the tank.
If you never want the ability to pull an end dump, than this is not necessary.
On your lowboy you should have a diverter valve that you switch to run off of a wet line versus your pony motor. Make sure you check into this as well (per your lowboy instructions).
Plumbing diagrams are available through websites like Parker, and others that sell pto and pumps. We purchased a kit that included the pto, pump, filter base and filter, and tank, and then had the hoses made up after we measured for length and fitting requirements.
On the pto's, we have two types: one that is cable controlled, and one that is air regulated. I was leery of the air regulated one at first, as it not only engages the pto, but also controls the lift valve operation using air, but we have had no problems with it.
Another thing to mention is that we have a larger line going to the lowboy than the return. We did this to make sure we had enough volume to run an end dump (one line). The lowboy did not require that much volume, so we used a smaller diameter hose for the return.
We were constantly having issues with the pony motor and pump, or running out of gas at exactly the wrong time, and are really glad that we put the wet kit on. There is a fair bit of expense to add the wet kit, but I think you will be glad that you did.
Other folks on the forum will surely have more information for you, but in general, if you go to your supplier of wet kits and tell them what you are doing, they should be able to guide you through what is needed. The lower volume pump that you are receiving from your friend should work great for your lowboy!