A Boxshall is mentioned several times in the Londoner. In that it confirms that he was transferred to the Tank Corps. 

There is a medal card for a Henry G. Boxshall in the Tank Corp but it makes no mention of prior service in the 25th. 

A postcard held by Russell Ridout is addressed to "H.G. Boxshall, 4 Co., 7th Platoon, 2/25th London Cyclist Battalion". Also in the photo album of Russell's grandfather, Stanley Ridout, is a signed photo "H.G. Boxshall as pictured here.

The Londoner 

Vol.1, No.4, Feb 1917,  pg.82
The motor cyclists have been transferred en bloc to the H.S.M.G.C. as gunners and drivers to the Tank Section and ordered to strike their stripes.

Vol.2, No.3, Jan 1918, pg.80.
Old "D" Coy. will be pleased to hear that G. Boxshall, who was wounded near Ypres on August 19th, is getting quite well again. He with Bill Bowes and other members of the second went to the M.G.C. for duty on tanks.
(Says "G". Boxshall but perhaps a mistake when the postcard and photo are clearly "H.G.")

Vol.2, No.6, Jul 1918, pg.158
Boxshall, who was wounded last August, has been in Blighty ever since.

Vol. 3, No.4, pg.106
Pt. Boxshall was demobbed about three weeks ago, and just came to see me for a few minutes, before he went. He seems to be all right, and quite satisfied with married life.