Good work with the photos. I agree with what has been said so far. The UN collection looks like a high quality collection that someone took good care to put together. (But unfortunately as others have said, UN stamps have not held their value. Here is a collection from
ebay that just sold last week for $52
https://www.ebay.com/itm/137554191997 that looks fairly complete through 1982 including some of the better items. Yours could possibly have more value, into the $100s depending on how modern it runs and whether it has any scarcer varieties, errors, or specialty items like sheets signed by the designers.
If you have any receipts or inventory or purchase records, that will help to identify any valuable stamps. If there are no records, chances are this is just a fun hobby collection that gave the man much enjoyment for a low cost, and therefore doesn't have a big monetary value today.
You said the Liberty album is not complete, but what do the first few pages look like? Are there a lot of stamps in there before 1900, or is it just what you have shown in the photos?
As for an app to quickly identify catalog numbers and what country a stamp is from, Google Image Search does quite well, if you have the Google app on your smart phone, or right-click on a photo in Chrome and "Search Image with Google Lens". As others have said, it cannot identify common versus rare varieties, or condition, or counterfeits, but can be a helpful head start to get you going in the right direction.