Since there's a solicitor involved, I assume that he/she is acting as executor of the estate (or, if there was no will, he/she is seeking letters of administration on behalf of the boy). In which case, the solicitor will be responsible for paying all of the deceased person's debts and the funeral costs from the estate before making the remainder of the money available (through a trust fund) to the boy.
i.e. There is no obligation upon your friend to pay for the funeral. It should be funded from her partner's estate (which includes the insurance payout). The only exception might be if she'd already arranged a massively expensive funeral. In which case, the estate would only be required to meet the basic costs, with your friend paying the excess.
Ultimately, nobody can be compelled to pay for a funeral. If nobody is willing to pay, the local authority is responsible for arranging, and paying for, a basic funeral. (NB: Local authorities aren't obliged to take over the costs of a funeral which has already been arranged by somebody else). They can then seek to recoup their costs from the estate of the deceased person (but not from any relative or partner).
Chris