I am assuming the deceased was domiciled in England, and thus the use of english solicitors. If that is so, your whereabouts should have no impact on the situation.
Replacing share certificates does not happen anymore. All he needs do is write to the company registrars and confirm the holdings - everything is now held on the paperless Crest system. Indeed, sounds to me as if he is struggling with this so I would be inclined to suggest he gets a stock broker to sort it out.
As for the wife - she was left a specific gift of the house. Specific gifts are always paid out before the residue (which is what you get, I think) and she has the right to sell it or retain it as she wishes.
It can take several years for an estate to be sorted out. Mind you, this does not sound unduly complicated so it is possible that it is the solicitor who is dragging his heels.
Write to the solicitor and ask him for an update on the present position. Leave it 28 days. If he does not respond, write a letter asking him if he is still instructed by the executrix and explain that in view of the delays and lack of info you are considering applying to the Probate Registry under s25 Administration of Estates Act 1925 for an inventory and account and holding his client personally responsible in costs. I've never known a letter threatening that not to have the right results.