Always good to know how the Jetronic woks and its weak areas though for the inevitable problems that will occur with it later

Given the car has been laid-up for a while it could be down to muck and gum from old, stale petrol becoming dislodged and bunging things up... Fresh petrol is an excellent solvent for such deposits...
I'm thinking that if there is starvation arising from any cause then the initial strong enrichment (by opening the injectors for longer) will allow a start but as soon as the mixture strength is wound back after a successful start - and it does happen quite rapidly on an Jetronic system - then the mix is too weak to sustain running even though the ECU believes the mix is 'right' for the prevailing conditions...
I take it the fuel filter has been absolved of guilt? That will easily get blocked by old fuel residues...
Mike, the problem with the AFM is often intermittent contact with the cermet track so your advice is good... There is a test you can do involving a 9v PP3 battery and a meter to ensure the track is good across the range. It should rise and fall linearly...
The other problem with the AFM is the spring goes weak and this causes the engine to run rich across the range...