I need to determine the constitution of an organic molecule by several spectra like 1H NMR, 13C NMR, COSY, HMBC ,and HSQC.
Typically, both two- and three-bond 1H–13C couplings appear in HMBC spectra, with three-bond couplings tending to be more prominent. The presence of other atoms in the path, e.g. oxygen, doesn't affect this. So, the three-bond coupling you have indicated is very likely to show up in the HMBC spectrum, as a cross peak at (f1, f2) ≈ (180 ppm, 4 ppm).
If all you are looking for is structural confirmation + assignment of 1H data (which would be typical if this was a product you expected from an experiment), I'd suggest that you don't necessarily need 2D data. The multiplet structures should contain more than enough information.