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A Will is a private document, which only the Executors and beneficiaries are entitled to see, until Probate has been granted.
Once Probate has been granted, the Will becomes a public document and any member of the public can apply to the Probate Registry for a copy, for a nominal fee.
How long does Probate take? Well, it all depends on how complicated the Estate is. If there is any Inheritance tax (IHT) to pay (where an Estate is valued over £325,000) it can take a good 6 months before Probate is obtained. If no IHT is payable, then Probate is normally granted after 3-4 months.
What i therefore suggest you do is to carry out a postal application to the Leeds District Probate Registry for a Standing Search. This means the Probate Registry will send you a copy of the Will as and when Probate is granted. The link to their website is as follows-
https://www.gov.uk/wills-probate.../searching-for-probate-records
I hope this assists and answers your question.
Kind Regards
AL