You will want to install Money Plus Deluxe Sunset onto the new computer. Download the installation file from the link in the second post on this forum.
So copy the *.mny and *.mbf files from the old computer into the Documents folder or other folder on the new computer. Note that you will want to change the backup filenames and paths to match what exists on the new computer.
Note that Microsoft Money Online Quotes from Gaier Software can let you download quotes easily if portfolio tracking is important to you. Free trial, and one-time $10 after trial. PocketSense can download transactions and maybe end-of-day closing prices.
hleOFXquotes also lets you download quotes. Those two are free.