The limbo period while switching between Tier 4 and Tier 2

[shue23]

Hello, I am currently on a Tier-4 visa which is valid till Dec 2019. I have finished my postgraduate degree programme and will graduate in July. My employer is currently in the midst of applying to become a visa sponsor, and thereafter issue me with CoS. Given that we've missed the current cycle of CoS issuances (I understand it closes on the 5th of each month), I'm expecting my CoS to arrive on 11 June.

I am actually going back home from 3 June to 6 July, and wanting to re-enter on my Tier-4 visa when I return for graduation. Am I likely to encounter any issues at customs? What sort of documentation would be helpful at the customs -- a letter of offer from my employer perhaps? Am I allowed to sign employment documentations already at this stage, although I haven't made my Tier 2 application? I was thinking that employment documentations will explain my case clearly at the customs.

I can only make my Tier 2 application in July, after I've received my degree certificate. While the Tier-2 visa application is in process, can I be employed on my Tier-4 visa? Theoretically it is school vacation now so I can work full-time on Tier-4 first? I'm trying to determine if it's worth the 500quid to do the priority service, or can I be gainfully employed full-time as a Tier-4 while the Tier-2 application slowly processes itself. Does anyone know how this will work?

Thanks in advance!