The UK Citizen spouse/partner can claim Child Benefits in his own name.
See the HMRC booklet
Child Benefit if you are coming from abroad or going abroad
Tax credits were introduced in 2003, and the immigration rules were subsequently modified in 2005.
The rule change in 2005 affects couples where one partner is not subject to immigration control (eg. UK Citizen or permanent resident).
The rule addresses both working tax credits and child tax credits.
Under the rule, a couple may claim both these credits without jeopardizing any immigration status of the person subject to immigration control.
Means, a couple can claim child tax credits and/or working tax credits as long as one partner is a British citizen or otherwise exempt from immigration control.
When claiming Child Tax Credit the UK Citizen partner should have ticked the box for themselves as the claimant.
The Tax Credit application will automatically be a joint application at the request of HMRC. Again no problems
