It all begins with Boccherini supposedly owning this 1709 Stradivarius cello and later being "obliged by his straitened circumstances in the last years of his life to sell" it to an unknown purchaser. Any trace of the instrument is then lost until mid 19th century when it reappears in the hands of Sebastián de Borbón, who left it after his death to his nephew, the Duke of Hernani, to disappear again until the end of the Spanish Civil War (1931-1936). Finally, composer Juan Quintero (1903-1980), who had bought the cello at an auction at a very low price (since the instrument was quite damaged), offered it to Gaspar Cassadó to be repaired and used in his performances.

We are not concerned here about what happened to this instrument after the presumed selling by Boccherini. Our only interest lies in the very first lines of this "fairy tale", that is: Did poverty force Boccherini to sell his cello (regardless of its luthier's mark)? Did Boccherini actually own a Stradivarius cello?
The answer to the first question is: Absolutely NOT.
The answer to the second question is: Most likely NOT.
We must insist (once more) that Boccherini had never experienced any "straitened circumstances" during his adult life. His economic situation varied from being "well off" to being "opulent", so he was never "obliged" to sell neither his violoncello nor any other patrimonial item.11
As for the second question, we have nuanced the NOT response with a "most likely" clause for the simple reason that this kind of negative evidence does not exist (or is extremely seldom found). It is hardly conceivable to find a document certifying Boccherini never had a Stradivarius. For the same reason, we should not expect to find any statement guaranteeing he never owned, for instance, a Guarnieri, either.
Negative evidence is only possible through a reasonable exclusion by deduction, and this is what we intend to prove in this case.
By the end of the 1990s, José Antonio Boccherini (sixth generation direct descendant of the Luccan composer) and myself, working independently but almost contemporarily, found a notarial deed up to then never spotted, where the composer and cellist declared the three musical instruments he owned in 1778.12
The following characteristics of this document are very significant:

a) It has an absolute credibility, being a Capital deed signed before a notary or royal actuary;

b) It is (so far) the only known and trustworthy document mentioning what instruments Boccherini actually owned; and

c) It is dated when Boccherini was a mature individual in the middle of his active life

This kind of notarial deed was signed by the spouse to her husband's favour after the wedding when he had had children from a previous marriage. The document is intended to recognise the value of each and all the goods owned by him at the time the second marriage is sanctioned, in order to avoid future inheritance controversies.
We are in front of a long manuscript listing every single object (clothes, dresses, furniture, jewels, menagerie, cutlery, money, etc.), the composer possessed in 1787, stating their corresponding value in copper reales (period currency in Spain. 1 real = 3 euros, or 4.5 US $, approximately).
Under the epigraph "Alajas" ("Jewels", that is showy objects, although misspelled for it should read "Alhajas"), we find the following three items:

Ingrandisci

11 See, among other evidence, the micro-econometric analysis of Boccherini's domestic welfare in Chapter XVII of Tortella, J.: Boccherini, un músico italiano en la España ilustrada, Sociedad Española de Musicología, Madrid, 2002, pp. 423-469.

12 Maria Pilar Joaquina Porreti's Capital deed to Boccherini: Archivo Histórico de Protocolos de Madrid (Historical Protocol Archive of Madrid, Spain): Protocol 20.771, pp. 101-109, April 26, 1787, Notary: Antonio Martínez Llorente. Boccherini and Porreti had been wed eight days earlier.