他一收到我的信就给我回信 英语怎么说

太多种了，列举如下：
1）On/Upon receiving my letter, he wrote back to me.
2) He wrote back to me as soon as he received my letter.
3) He wrote back to me immediately/directly/instantly he received my letter.
4) He wrote back to me the minute/moment/second/instant he received my letter.
5) Hardly/Scarcely had he received my letter when he wrote back to me.
6) No sooner had he received my letter than he wrote back to me.
7) He had hardly/scarcely received my letter when he wrote back to me.
8) He had no sooner received my letter than he wrote back to me.

He will write to me as soon as he receives my letter.
as soon as一...就
write to sb.给某人写信

He wrote to me as soon as he received my letter.

Receiving my letter,he will write back.
Once he received my letter, he will write back as soosn as possible.