  Here the gravitational lensing in strong field limit of a Schwarzschild black
hole with a solid deficit angle owing to global monopole within the context of
the $f(R)$ gravity theory is investigated. We obtain the expressions of
deflection angle and time delay in the forms of elliptic integrals and discuss
the asymptotic behaviour of the elliptic integrals to find the explicit
formulae of angle and time difference in the strong field limit. We show that
the deflection angle and the time delay between multiple images are related not
only to the monopole but also to the $f(R)$ correction $\psi_{0}$ by taking the
cosmological boundary into account. Some observables such as the minimum impact
parameter, the angular separation, the relative magnification and the compacted
angular position have been estimated as well. It is intriguing that the tiny
modification on the standard general relativity will make the remarkable
deviation on the angle and the time lag, offering a significant way to explore
some possible distinct signatures of the topological soliton and the correction
of the Einstein general relativity.
