There does seem to be a driver for it in the AUR:
$ pamac search L2350
brother-hll2350dw 4.0.0-2 AUR
Brother HL-L2350DW CUPS driver
Which can be easily installed using:
pamac build brother-hll2350dw
Hope it helps!
a Reminder: While use of the AUR is possible, it’s neither recommended nor supported. See:
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