During the install with a restore from backup using the LXP, the Analyze software installer will ask you for a secure store password, it will then create a new secure store and store your (new) password encrypted in the cust.prop file.
After installation, you then replace the secure store.jks file with the one from the Windows system. You will then have to update the secure store password in the Linux system's cust.prop file to match what it was on the Windows install.
The development team have tested this restoration scenario. However, you will need to confirm the correct operation of the data flows that have been running on the Windows system. The Windows file paths for local files in node properties, data flow properties and run properties may contain backslash ('\') characters for the directory delimiters which will be interpreted as escape characters on a Linux system. Also it is likely that references to file locations on local drives will be different between the Windows system (e.g. D:\foo\bar) and mount points on the Linux system. You may want to consider using the Search capability to identify property values that may need to be updated.
It is difficult to recommend using the restore from backup method vs. exporting all data flows and importing & recreating any schedules. It depends on the composition of the data flows and schedules that have been created on the Windows system. A high proportion of the time to test the correct operation of the Linux system will be assess the individual data flows are running as expected. Using the restore from backup method will have the advantage that the configuration of schedules will be retained. It will also mean that other configuration such as user profiles, permissions, etc will be retained. As an interim test step you may want to consider importing individual data flows into the Windows system and testing them for potential path issues, etc. This would allow you to collate the set of confiuraiton items that would need to be modifed if the restore option is used for the actual migration.