Van der Krogt (stating that: "The smallest globe [by Adams, i.e. 2¾-inch] is unsigned") illustrates and describes a similar globe as Ada 1 ("Cook's first voyage ... is indicated with the legend Cooks Track 1760") mounted on a tellurian signed by George Adams and describes another three similar unsigned globes (Ada 2-4) mounted in an armillary sphere, tellurian (both signed by George Adams) and a planetarium signed by Nairne & Blunt. A similar globe is described as item 5.16 in The World In Your Hands: "This anonymous pocket globe has often been ascribed to the work of George Adams Jnr since an armillary sphere signed by Adams uses this pocket globe. However recent research has shown that the origin of these gores is Hermann Moll's pocket globe of 1710". The label of 5.16 is illustrated by Schmidt (p. 3) and is the same as that on the present example.
Item 5.13/5.14 would also seem to be similar: "the terrestrial showing the track of Capt. Cook's first voyages (1768-71 but incorrectly dated 1760) and the discoveries of his second and third voyages, i.e. New Caledonia, indicating that the globe was made in or after 1784 when Cook published his account of the third voyage".
Given this rather confusing plethora of possible sources, one hypothesis could be that John Senex (who is described in The World In Your Hands as "very much a rival to Hermann Moll") bought up Moll's plates after his death in 1732. It is known that Senex's widow sold off his plates in 1755 and "George Adams acquired the plates for the pocket globes". Van der Krogt describes a tellurian using a Senex globe made by George Adams (Sen 1), so it could be that Adams used a re-engraved version of Moll's globe, from Senex's stock, for the items Ada 1-4.