Quick help needed: what would you do?

[msfreud]

My tenants are due to move in today but their deposit and fees etc. were only transferred to the lettings agents account from a French account today and are unlikely to arrive until early next week.

Tenants are in letting agents office. Agent is asking me would I let them move in today?

Human side in me says yes, business side says no.

Lettings agent has paperwork from bank showing the money has been transferred. But can a bank transfer be reversed or something?

I would be wary - normally you need cleared funds before the tenancy can commence. Did the bank communicate direct with the letting agent? Also, what about the rent: is that going to be coming (late) from a French bank account every month?