this may help.
NEW ZEALAND EXPEDITIONARY FORCE INFANTRY REINFORCEMENTS
Dates of Departure from New Zealand
Main Body including 1st Reinforcements 16 Oct. 1914
2nd Reinforcements 14 Dec. 1914
3rd Reinforcements 14 Feb. 1915
4th Reinforcements 17 April 1915
5th Reinforcements 13 June 1915
6th Reinforcements 14 Aug. 1915
Advance Party - 1st & 2nd Battalions N.Z. Rifle Brigade 18 Sept. 1915
7th Reinforcements 1st Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade 9 Oct. 1915
8th Reinforcements 2nd Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade 13 Nov. 1915
9th Reinforcements 3rd Reinforcements to 1 st & 2nd Battalions & Advance Party of 3rd & 4th Battalions N.Z. Rifle Brigade.3rd & 4th Battalions, plus 1 st Reinforcements to 3rd & 4th 5 Feb. 1916 Battalions N.Z. Rifle Brigade. 8 Jan 1916
10th Reinforcements 4th Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade 4 Mar. 1916
11th Reinforcements 5th Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade
2nd Reinforcements to 3rd & 4th Battalions N.Z. Rifle Brigade I April 1916
12th Reinforcements First Draft 6th Reinforcements to 1st Battalion N.Z. Rifle Brigade I May 1916
12th Reinforcements Second Draft 6th Reinforcements to 2nd Battalion plus
3rd Reinforcements to 3rd & 4th Battalions N.Z. Rifle Brigade 6 May 1916
13th Reinforcements 7th Reinforcements to 1st & 2nd Battalions plus
4th Reinforcements to 3rd & 4th Battalions N.Z. Rifle Brigade. 27 May 1916
14th Reinforcements 8th Reinforcements to 1st & 2nd Battalions plus
5th Reinforcements to 3rd & 4th Battalions N.Z. Rifle Brigade 26 June 1916
15th Reinforcements First Draft 9th Reinforcements to 2nd Battalion plus
6th Reinforcements to 3rd Battalion N.Z. Rifle Brigade 26 July 1916
15th Reinforcements Second Draft 9th Reinforcements to Ist Battalion plus
6th Reinforcements to 4th Battalion N.Z. Rifle Brigade 29 July 1916
16th Reinforcements First Draft 10th Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade 19 Aug. 1916
16th Reinforcements Second Draft 7th Reinforcements to 4th Battalion N.Z. Rifle Brigade 20 Aug. 1916
16th Reinforcements Third Draft 7th Reinforcements to 3rd Battalion N.Z. Rifle Brigade 21 Aug. 1916
17th Reinforcements First Draft 8th Reinforcements to 3rd & 4th Battalions N.Z. Rifle Brigade 23 Sept 1916
17th Reinforcements Second Draft 11th Reinforcements to 1st & 2nd Battalions N.Z. Rifle Brigade 25 Sept 1916
Reference came from here.
http://www.diggerhistory.info/pages-badges/nz-reo-badges.htmAlan NZ