The New Zealand team arrived home on Saturday and now the entire contingent will undergo 14-day mandatory isolation.
If all goes well, the South Africa-born Wagner, who is No 4 in the ICC Test rankings, should be lining up for his adopted country in the final of the World Test Championship.
On Saturday, Henry and Wagner picked three wickets each as New Zealand dismantled England's batting to sniff victory on Day Three of the second Test.
Though he is excitedly looking forward to play in the WTC final, Wagner said he would not like to let the occasion get the better of him.
Wagner, ranked number three in the world among Test bowlers, trained with the Dukes ball in Lincoln before departing for England.
New Zealand pacer Neil Wagner received his first dose of the Pfizer/BioNTech vaccine on Tuesday at Tauranga Hospital.
The Caribbean visitors have historically been known for their own fast, intimidatory bowling, but were troubled by Neil Wagner's rising deliveries in the first Test.