Are you hosting this file over a network such that you open the file as a client of this hosted file? (as opposed to opening a file stored directly on your computer).
If so, client side found sets, including sort orders are not and cannot be saved when you close the file.
You'd need to create your own system that saved such info to a table with one record for each user that a script could use to restore the found set when you either open the file or access a particular layout.
The filemaker program I am working on is a single use but it is part of a server system. I don't know what you mean by setting up my own system. I am the only user of this program.
The filemaker program I am working on is a single use but it is part of a server system
Which still makes it a system hosted over the network and you as a client of that database. The found set will not be saved when you close the file.
You'd need to create a script that stores the information needed to recreate your found set, sort order and current record to fields in a table of the database and one that uses that info to recreate the found set and sort order.
There are two basic ways to "save a found set". You can save a list of IDs from the current found set or you can save the criteria that you used to find the records. Then add the name of the field or fields that you sorted on and the ID of the current record and you have the basic ingredients for recreating a found set.
But you'll need some basic database design skills to make this happen.