If my recollection is correct, RR worked from home in the past. I'm thinking that might be the reason he got in the habit of using the unfamiliar program to keep track. Unless self-employed or with complicated finances, the average person doesn't need them anymore. Banking records for income and disbursements are all posted online and can be accessed with any computer although they may ask for additional security information with a new computer or IP than used in the past.
Transferring his program and information to another computer might be difficult if not impossible without installing RR's program on the newer one or another program that is compatible. What you might be able to do is print out or copy the input information, accounts, addresses, phone #'s etc. so you can get in touch if there is a problem. Quicken is the most popular finance tracking program that has been around for a very long time but there are many others.