Help with ESA claim

i am trying to help my sister in law who is struggling with stage 4 lung cancer, she now has a DS1500 and gets PIP but I can’t get the ESA sorted because of a shortfall in her NI contributions. The qualifying period is 2016/2017 and 2017/2018 but she only started being self employed in Aug 2016.we can pay the shortfall but if we pay it we don’t know if she will qualify, as only 17 months. Can anyone help with where to go for help asshe really needs this money? Thank you