First, you would be wise to make sure your mother's assets are in a Trust so that probate will not be necessary. On the other parts, if the estate is over 5.25M, I dont want to comment and your mom should really be seeking advice from an experienced estate planning attorney in her area. If the amount is less and taxes are not going to be an issue, having everything pictured and inventoried could be of great assistance.
There really isnt a ton you can do as a prophylactic measure or to prepare. What would be helpful would be a small joint account outside the trust so you have funds to get up and running to hire an attorney and deal with funeral expense and such. In addition, you should ensure that your mother has proper powers of attorney in place and the nomination of a conservator or guardian should she lose capacity and require one.
You may also want to find out from your mom where she keeps all important paper such as tax returns, insurance policies, records of bank accounts, etc.
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In the first instance, if your mother has been working with an estate planning attorney, that attorney should be able to provide you with some resources. Are you the only beneficiary or are there multiple beneficiaries who would receive a portion of her estate? If the latter, and if your mother is still in good health, it would actually be very helpful to the future Executor (you) to have her specify who should get which pieces of art and jewelry. She would have to execute a new will or codicil to make this binding (or by memorandum if she has a trust), but it would go a long way toward distributing her estate later.
Separately--and I don't know if she is in a terminal medical condition and this is why you are trying to line up resources now--but there are art and jewelry appraisers who can help you determine value for purposes of dividing up the estate by percent value. Whether they will still be in business when your mother passes or not, I don't know.
Finally, if your mother does not have an estate planning attorney (which she should, especially if she has a sizeable estate), then you can start interviewing probate attorneys in the county where she resides and be well on your way to selecting one to assist you at the appropriate time.
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All good advice from the other attorneys - your mother's current lawyer should be willing to help his client (mom) and you have a smooth transition (with her consent of course). I would also add that if there is a present relationship with a bank or financial adviser that person can be brought into the conversation now, as well as appraisers and experts on collectibles.
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Suggest she name you and the attorney as co-executors and/or co-trustees.
This would allow equal authority and the attorney to do a lot of the work.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.