If the employees are on Universal Credit then this will cause problems there too.
SA system not setting correct flags on PAYE system and PAYE system processing accordingly
Part of the problem is that you, for reasons possibly outside your control, paid her for Nov, Dec and Jan and reported these in February. In her Nov, Jan and Feb UC assessments she will have received earnings and full UC. You send in the Feb FPS and HMRC send that to DWP. The UC system looks for the latest FPS, February, and the last one that it used. In this case there isn't one. Over the four months it is possible the correct amount of UC has been paid. Whose fault that she has had her cash flow mangled is an interesting question.
Whichever P45 is handed in will determine the code. Therefore make sure it's the one with the full code. That will ensure that cumulative PAYE is operated. It will probably still be a P800 case at the end of year
Unless the payer or recipient chooses to delay the payment or the more complicated rules for a director. S686 ITEPA 2003
It's pretty possible he wasn't due JSA. If he's started drawing the pension then it's likely to be looked at as capital or income depending on what he draws. That's before you get to working and claiming JSA.
Which came first and was the pension the first extraction from the scheme?
Your payroll software ought to do that for you. In effect you give an extra week's, fortnight's or lunar month's allowance depending on pay frequency. HMRC will then claw that back in the P800 or SA process.
The employer can be held responsible for payment of any tax underpayment arising from the incorrect operation of PAYE. HMRC can direct that the employer pays subject to usual caveats. Deliberately changing the code wouldn't fit the caveats.
If he's a new starter with you and has handed you a P45 then you use the P45.