  We consider the isotropic spin-$1/2$ Heisenberg spin chain weakly perturbed
by a local translationally- and $SU(2)$-invariant perturbation. Starting from
the local integrals of motion of the unperturbed model, we modify them in order
to obtain quasi-conserved integrals of motion (charges) for the perturbed
model. Such quasi-conserved quantities are believed to be responsible for the
existence of the prethermalization phase at intermediate timescales. We find
that for a sufficiently local perturbation the quasi-conserved quantities
indeed exist, and we construct an explicit form for the first few of them.
