Unit They Belonged To?

One thing I've always wondered about when I've watched this film was just what Division Stryker's squad belonged to.

At the start of the film, Dunn's narration says that they had been fighting on Guadalcanal, before being sent to New Zealand for rest, replacements and to retrain for further combat roles.

Now, there were two Marine Divisions at Guadalcanal. The 1st and the 2nd. The 1st had been there since the initial landings in August of 1942, and been pulled out in December. The 2nd Marine Division had a more piecemeal history. The 2nd Marine Regiment had landed with the 1st Division men in August, with two other regiments (the 6th and 8th) arriving in the ensuing months. The 2nd Marine Division then was the main Marine element at Guadalcanal until the island was officially secured in February of 1943.

The 2nd Marine Division was then sent to New Zealand until the Tarawa campaign that November.

So, I would naturally assume Stryker and his squad had been in the 2nd Marine Division, except that when Stryker meets the squad, Thomas says he thought Stryker had been in "the First". Stryker replies that he was. Stryker was either referring to the 1st Marine Regiment or the 1st Marine Division.

Now, it would be conceivable for an experienced NCO to be sent to another division -especially with new men coming in. However, would his entire unit be sent with him?

Likewise, after Tarawa, the squad is sent to Hawaii to retrain for Iwo Jima. It's supposed to be the 5th Marine Division as that was the division that put up the flag. As well, the 5th Marine Division was a new unit, but had combat veterans make up 40% of its compliment. Again, was Stryker's entire squad transferred intact from the 2nd Marine Division to the 5th Marine Division? Does anyone know if this was ever done in World War II? (Entire units on a squad, platoon or even company level transferred to new divisions to leaven them out?) Or, was this something that the writers simply went with so that they could have Stryker have fought on Guadalcanal and show the squad fighting on Tarawa (which was perfect for the purposes of the film, as it was a savage but relatively brief -76 hours- battle)?