The widow Eugenie Caroline Theodore Rinsby died in Lowerhill nr Richmond, London

[jonwarrn]

There might be a faint hope that the date of death could be written along with the probate details on or with the original will (apparently it was written in French, it should be at TNA)

I wouldn't be confident, but you do see it in some courts at that time, i.e. here on this Lancashire will proved in 1810 in the Chester Consistory Court
https://www.familysearch.org/ark:/61903/3:1:S3HT-D4MS-2P

I don't think it would be given in a Probate Act Book entry in 1810, like we have them from 1858 in the annual national probate calendars.

Depending on the value of her estate, the death duty register entry might be useful 
Available on microfilm at TNA or at a LDS FamilySearch Centre

Madame Rinsby doesn't seem to be in the Richmond burial register. They do have a few more exotic names than is the norm in them, a Count Alexander du Pont was buried there in 1805.

[PatLac]

Cholmley's Estate, between Portsmouth Road and river Thames, Long Ditton.

https://www.exploringsurreyspast.org.uk/collections/getrecord/SHCOL_2249_1_1_1_1

Copy of affidavit by David Dundas of Richmond, surgeon, and Catherine Sayer, servant to Anne Jesse Cholmley of Richmond, to the effect that they witnessed Anne Jesse Cholmley signed her consent to a bill (missing) annexed and that she was unable to appear through illness.

https://www.exploringsurreyspast.org.uk/collections/getrecord/SHCOL_504_12_1_1_1


One place to look for her burial record could be Thames Ditton St. Nicholas

https://www.surreygraveyards.org.uk/elmbridge/thamesdittstl.shtml

[PatLac]

I wonder if this was Eugenie?

The twelve items in the Beaupoil de St. Aulaire letters concern the social activities and family news of a female French émigré living in England at the turn of the nineteenth century. The letters are primarily personal in nature, but also discuss French politics, language, and culture, particularly in reference to Napoleon Bonaparte and the French Revolution. The letters, many of which do not address the recipient by name, all appear to be written to the same person, possibly a Miss Phipps, who is living with Mrs. Cholmley "under the hill" at Richmond, Surrey.

Dates
Creation: 1803-08 - 1803-10


https://archivesspace.williams.edu/repositories/4/resources/466


Anne Elizabeth Cholmley Phipps was born on 19 May 1788, the daughter of John Constantine Phipps, Baron Mulgrave (1744-92; ODNB), naval officer, arctic explorer, and politician, and Anne Elizabeth Phipps, née Cholmley (1769-88). Her mother died in childbirth leaving her as her father’s sole heir. After her father’s death in 1792, Anne Elizabeth Phipps grew up under the guardianship of her widowed grandmother, Anne Jesse Cholmley (1748-c.1812). Her guardian’s consent was needed and obtained when, still a minor, Anne Elizabeth Phipps married Sir John Murray, eighth baronet (1768?-1827; ODNB) in 1807.

https://btw.wlv.ac.uk/authors/1103

The place was literally UNDER THE HILL, wrongly translated Lowerhill.

BURIAL: Parish: Richmond, St Mary Magdalene; John Jepson; 62 years; Burial Date: 8 Jun 1838. Archive Reference No: P7/1/12; Text: St. Mary Madgdalene: Burials in the Parish of Richmond in the County of Surrey in the Year 1838; Entry No. 927 Text: John Jepson F 36 N Abode: Under the Hill; When Buried: June 8th; Age 47; Off Min: G. Coulcher. Surrey, England, Burials, 1813-1987; Ancestry.com; Publisher: Ancestry.com Operations, Inc; Publisher Date: 2013; Publisher Location: Provo, UT, USA; Original data: Anglican Parish Registers. Woking, Surrey, England: Surrey History Centre.

https://www.wikitree.com/wiki/Jepson-25

Another resident of "Under the Hill"

https://www.open.ac.uk/Arts/reading/UK/record_details.php?id=17692

And here:

https://leicester.contentdm.oclc.org/digital/collection/p16445coll4/id/366272/rec/2

Lady Caroline Murray lived at Under the Hill, Richmond in 1855.

https://leicester.contentdm.oclc.org/digital/collection/p16445coll4/id/366271/rec/2

https://www.findagrave.com/memorial/270047091/caroline-murray#view-photo=294585467


So maybe this is the place to enquiire for her burial place?

https://www.surreygraveyards.org.uk/richmond/richmondstmm.shtml

[PatLac]

A house being sold at Under the Hill, Richmond, on the Morning Chronicle 14 July 1806. There is another advertisement but this one is free 

[PatLac]

You could try to find this book.

"List of Graves in Vineyard Passage Burial Ground’ (Judith Filson 1985: Richmond Local Studies Collection)"

https://richmond.gov.uk/media/21455/vineyard_passage_burial_ground.pdf

Coincidentally, the Reverend died the same year (1806).

In the Vestry Minutes for 20 October 1806, mention was made of the natural springs
that were common on the Hill:
“Resolved that the Reverend Mr Wakefield and the Church Wardens be requested to
examine and report to the Vestry their opinion of the necessity of the new burial
ground being drained from the great flow of land springs therein”
Nothing appears to have happened about this, probably due to the death of the
Reverend Wakefield in that same year.

Good luck with your research and let me know if you find her!

Cheers.

[PatLac]

Despite your lack of feedback I am insisting on posting because I keep finding interesting things that might be pertinent to your question.

Abraham Trembley et autres précepteurs suisses en Hollande. Correspondances (1733-1801)

Page 454

Ravanel, Mlle : 390, 392

https://classiques-garnier.com/export/pdf/abraham-trembley-et-autres-precepteurs-suisses-en-hollande-correspondances-1733-1801-index.html?displaymode=full

https://classiques-garnier.com/abraham-trembley-et-autres-precepteurs-suisses-en-hollande-correspondances-1733-1801-preface.html?displaymode=full

[Axonais]

Dear PatLac,
Excuse me for coming back so retardingly. I was very busy these days. Yes I do appreciate your postings very much. I know Kees van Strien’s book already. His findings in Dutch archives are important.
I have to look at your other postings as yet. Miss Phipps was a daughter of Nathaniel Cholmley and Henrietta Catherine Croft. Nathaniel Cholmley married again to Anne Jesse Smelt, daughter of Leonard Smelt, mentioned in my query and mentioned by you. She is the Mrs Cholmley mentioned by Eugenie Rinsby in her will. Eugenie must have followed Mrs Cholmley to Richmond after Leonard Smelt’s death.
The Local Studies Library in Richmond (https://www.richmond.gov.uk/local_studies_collection) seems to have a film of Richmond burials in the beginning of the 19th century. I hope they can search them on my behalf.