  We show that Floer cohomology of an immersed Lagrangian brane is invariant
under smoothing of a self-intersection point if the quantum valuation of the
weakly bounding cochain vanishes and the Lagrangian has dimension at least two.
The chain-level map replaces the two orderings of the self-intersection point
with meridianal and longitudinal cells on the handle created by the surgery,
and uses a bijection between holomorphic disks developed by Fukaya-Oh-Ohta-Ono.
Our result generalizes invariance of potentials for certain Lagrangian surfaces
in Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer
cohomology under mean curvature flow with this type of surgery, as conjectured
by Joyce.
