They don't sell your type of filter in the UK so I had to look it up. It says it is rated up to 80 gallons which means you won't have enough filtration if this is the only filter you intend on using.
If you are swapping from one tank to another and one tank is already cycled, you can save yourself a lot of time and hassle by transferring the existing filter from the old tank to the new one. As long as you don't turn the filter for too long , you should be transferring a healthy biological filter. It's always a good idea to use as much water from the old tank if possible, then you can transfer the fish from one tank to another without any problems.
However, it seems that you don't have enough filtration for your 150 gallon tank so you may have to do get yourself either another filter to make up the difference, or get yourself a filter that will do the whole tank. Personally, I prefer the idea of using the existing biological filter, even though it isn't quite enough, it will certainly give you a head start.