:Thank you for your answer to my question. Maybe I have more informations for you:  
 * On this site] there is some information about his father Timothy, vicar of Bierton.  
 * On this site is the information I mentioned above about his parent and his sister. 
 * And finally these letters also my interesting for you: 
 **a Letter recommending George Shaw to join Pacific voyage, received by Lord Sandwich, from Sir Francis Dashwood, Lord Le Despencer, 20 December 1771, written by his father Reverend Timothy Shaw. 
 **a Letter recommending George Shaw to join Pacific voyage, received by Banks from N. Wetherell, 24 December 1771,  
 **and finally Letter received by Banks from George Shaw, 12 January 1772 (Series 06.183) written by George Shaw himself 
 :My very best wishes, TomCatX, 31 October 2005