Multiple Macs and One Database File
How to allow multiple users to use the same database file (but not at the same time), or access the same database file from different Mac computers
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Locate the "TimeSlice.sqlite" database file (open the TimeSlice preferences, click the Saving tab, click Reveal Database File).

Quit TimeSlice.

Move the TimeSlice.sqlite" database file anywhere you'd like.  This can even be on a shared folder, such as a DropBox shared folder from DropBox.com (DropBox is convenient way to share files over multiple computers, and is free for lightweight use).

Select the database file "TimeSlice.sqlite" in its new location, and using the Finder, make an alias of the file.

Move the alias file back where the original database file resided.

Rename the alias file from "TimeSlice.sqlite alias" to "TimeSlice.sqlite".

Start TimeSlice.

Caution: only one TimeSlice user should access the database file at one time.  In other words, the database file is not designed to be multi-user friendly.