Can any native speaker of British English help me? (suggests vs. will suggest)

[Sitifan]

1. He [suggests/will suggest] that she should leave the house at once.
2. He [suggests/will suggest] that she shall leave the house at once.

#1 is correct. Is #2 also acceptable in British English?

Thank you very much for your reply.
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Thank you very much for your reply.

[Alan]

Hi,