Many thanks to you both - some useful addtional material for me to look at
I was aware that Stuart had replaced Villiers, (I think, I will have to look thru’ some notes I took, perhaps from Muir, "Britain and the Defeat of Napoleon...." that) Villiers had asked to be replaced: I do know that the family Wellesley were supportive of Stuart’s candidature and appointment.
Villiers reports Stuart’s appointment to W (mentioned in a despatch from Lord (Richard?) Wellesley) in WSD vol vi (1860) p 476 Villiers to W, Lisbon 23 January 1810
But what I don’t understand is how / why Villiers is back in Portugal in May 1811 and communicating with Wellington
According to Fryman, “Stuart sailed for Portugal at the beginning of February [perhaps February 2nd] and arrived in Lisbon on February 11th, 1810” p 36
Fryman reports that the following day apparently Villiers accompanied Stuart to the Regency Council to present his credentials and four days later left Lisbon.

Fryman, M Charles Stuart and the Common Cause: The Anglo Portuguese Alliance 1810-1814 (Phd Thesis Florida States University)

A perplexed Anthony