Hi Suzy,
If your friend is on IB ESR only then it is likely that she has no entitlement to Contributory, otherwise she would be on C with an IB top-up.
Once your friend and her partner move in together, his income and savings would be taken into account and counted as hers. If he has more than £6000, this would affect her ESA and payments would be reduced proportionally, £16000 and above would wipe out any payments completely. In addition, if the partner earns too much or works for more than 24 hours, ESA payments would cease.
24 hour work rule for ESA(IR) Asset rule for ESA(IR) If your friend is onC ESA with an IB top-up, the IB could be wiped out but the C payments would continue - whatever the savings, income or working hours of the partner.