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при первой возможности ударения
общ.	at the next opportunity (Andrey Truhachev); at the first opportunity (I will do it at the first opportunity.); as soon as ever I can (Anglophile); as accurate as possible (alenagorelkova); as soon as conveniently may be (oVoD); first thing (I can't help you now, but I'll do it first thing. 4uzhoj); upon availability (Bauirjan); when occasion offers (Alex_Odeychuk)
Игорь Миг	at the earliest; at the earliest moment; at the earliest possible juncture
бизн.	as soon as possible (dimock); as soon as practicable (Alexander Matytsin); as soon as they become available (Alexander Matytsin); on a first-available basis (transler)
делов.	at your earliest convenience (Leonid Dzhepko)
дип.	when the opportunity presents itself (financial-engineer)
Макаров.	at the earliest opportunity
ритор.	as soon as we can (Alex_Odeychuk)
чат., эл.почт.	ASAP (4uzhoj)
юр.	at the earliest possible opportunity (Alexander Matytsin); as promptly as possible (Alexander Matytsin); as promptly as available (Alexander Matytsin); as soon as reasonably practicable thereafter (Alexander Matytsin)
отправить "при первой возможности"
авиац.	FRAV (first available; код связи)
"отправить при первой возможности"
авиац.	first available

при первой возможности: 31 фраза в 9 тематиках

Банки и банковское дело	1
Бизнес	5
Военный термин	1
Идиоматическое выражение, фразеологизм	1
Макаров	3
Общая лексика	16
Официальный стиль	1
Экономика	1
Юридическая лексика	2