vice-, assistant, aide, duplicate, copy
副 centers on a secondary or supporting role: something that is vice-, assistant, or an aide. The duplicate/copy sense extends naturally from the idea of a secondary version that accompanies the main one.
副 combines 畐 (a container or vessel) with 刂 (knife). The original idea likely involved splitting or dividing a container, leading to the sense of a secondary or duplicate part. The exact historical development is uncertain.
A knife 刂 splits a container 畐 into two parts: the main part and its duplicate or assistant. Think of a vice-president who is the secondary copy of the president.
For フク, imagine a vice-assistant wearing a fuku (服, clothing) that is a duplicate of the boss's outfit: fuku -> フク.
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assistant; associate; vice-; sub-; deputy; substitute; auxiliary; supplementary; additional; collateral
side job; sideline; subsidiary business
side effect; adverse reaction
adjutant; aide; aide-de-camp
deputy head; deputy director; vice chief (of something)
by-product
suprarenal body; adrenal glands
subtitle; subheading
secondary
adverb
supplementary prize; additional prize; auxiliary prize; bonus prize
supplementary reader
assistant umpire; assistant referee
second in command (of an army)
grave goods; burial accessories
module subprogram
senior vice president
representative executive vice-president
collateral ligament
pseudohypoparathyroidism