I think there's two separate issues here that are possibly being confused.
In general, if you instruct a solicitor in relation to a particular matter and then change your mind and decide you want another solicitor to act for you in that matter, you're entitled to do that. You tell the first solicitor to send the file on the matter to the second solicitor. The first solicitor may (and invariably will) hold onto the file until all his fees and costs for acting in relation to the matter have been paid. So he bills you, you pay the bill, and then he sends the file to the second solicitor (after removing those parts of it which belong to him, the solicitor, rather than to the client).
But that's not what happened here.
The first solicitor was instructed in relation to the drafting and execution of the will. He completed that mattter; it's done and dusted. He billed the testator, got paid, closed his file and sent it to storage. There is no active part-completed matter which the second solicitor is now to take on.
The testator could have taken his will away and kept it at home, or in his office, or kept it wherever he liked, or given it to whoever he liked to store for him. But he didn't; he asked the solicitor who drafted the will to keep it in safe custody for him.
Right. Some time later, the testator dies and the executor wants to apply for a grant of probate. He instructs solicitor 2 to act for him in relation to that application. This is a new matter which has never had another solicitor involved in it, so no question arises of picking up another solicitor's file in relation to a part-completed matter. There is no reason, usually, why the executor's solicitor would need or want to see the file in relation to the drafting or execution of the will. All he needs is the actual will.
So, the solicitor who has custody of the will is asked to send it on. He does, and he charges a fee for uplifting the will from safe custody and delivering it. Subject to the fee not being excessive, that's not unreasonable.
Later on, solicitor no. 2 finds that he does need some information which is likely to be in the files of solicitor no. 1. So he writes and asks for it. That's a new request which has nothing to do with uplifting a document from safe custody. He's asking solicitor no. 1 to dig up his old file (which he will have in storage, but usually not in safe custody), go through it, identify and extract the relevant information, and send it on. Again, not an unreasonable request. Again, not unreasonable for solicitor no. 1 to charge a fee for it; this isn't work he has already been paid to do.
If solicitor 2 thinks that there may be more things on the file (other than the thing he is currently looking for) then at this point solicitor 1 can now be asked (and paid) to deliver the file, rather than the specific item now needed. But in fact all he is obliged to send on are the parts of the file that belong to the client; he can keep the parts that belong to him. So this requires him to go through the file and decide which items he must send on and which items he can keep, and this is work he is entitled to charge for. So you would think twice before asking for everything on the off-chance that other items might turn out to be needed.
Items belonging to the client:
• Original documents sent to the firm by the client
• Documents sent to or received by the firm as agents for the client e.g. correspondence with counsel or experts
• Final versions of documents prepared by the solicitor for the purposes of implementing the client's instructions e.g. agreements, court pleadings,
• Final versions of documents prepared by a third party and paid for by the client e.g. counsel's advice or expert reports
Items belonging to the solicitor:
• Documents prepared for the firm's own benefit or protection e.g. file copies of letters written to the client, notes regarding time taken or made for protective purposes regarding advice to the client
• Drafts and working papers
• Internal emails and correspondence
• Emails and correspondence written by the client to the firm
• Accounting records (disbursement vouchers, timesheets, etc)