Investigating the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msubsup><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>1855</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> exotic state in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</…

An analysis of the J/ψ→ηη′γ decay by BESIII collaboration claims observation an exotic state η1(1855) with IGJPC=0+1−+. To establish its C-parity partner η1′(1855) in picture KK¯1(1400) molecular state, we propose that J/ψ→η1′(1855)η(′) receives main contributions from final interaction KK⁎(K+K⁎−, K−K⁎+, K0K¯⁎0, and K¯0K⁎0). Specifically, K K⁎ J/ψ→KK⁎ decays transform as η1′(1855)η(′), exchanging a K1(1400). We predict B(J/ψ→η1′(1855)η)=(6.3−3.5+12.6)×10−6, B(J/ψ→η1′(1855)η′)=(6.5−4.6+6.6)×10−6, which can be studied J/ψ→K⁎K¯⁎η(′) decays.