Classes like the artificer can prepare a new spell list in 1 minute, can an artificer cast a long-duration spell such as false life (1 hour), and immediately prepare a new spell list while retaining false life's effects?
An Artificer cannot change their prepared spell list in 1 minute
Artificers prepare their spell list as follows:
You can change your list of prepared spells when you finish a long rest.
A long rest takes eight hours, (four if you're an elf).
During that long rest, in order to change your spell list you must spend time:
tinkering with your spellcasting focuses: at least 1 minute per spell level for each spell on your list.
However, these changes won't be in effect until you 'finish a long rest'.
That said, you can indeed 'cast a long-duration spell [..] and then immediately prepare a new spell list while retaining [its] effects'.
Unfortunately false life wouldn't work that well for this - as its duration is only an hour long, much shorter than the length of a long rest - but something like water breathing (duration 24 hours) would.