Recruitment Agencies in Singapore

Please mention in which field your husband is trying his luck as there are many Consulting firms with  their specialists in different job fields can help him. But again it depends on demand and supply at present market. Wishing him best of luck.

He's looking for a job preferably in shipping, export/import, sales, customer service.

Do some agencies match jobs with experience/education?

Thanks a lot in advance.

Singapore employment agencies are not a great help in finding jobs.
Unlike other countries, here they are just reacting to job ads (many of which you can find on the usual online job sites as well as with other agencies) by sending as many CVs as possible to them, based on simple keyword matches, and hoping one of them is selected so they earn a commission.
They will not go out of they way to assist or actively find something for a candidate.
So, while your husband should certainly register his CV with some of them, he should not put much hope into this.
The best way to find a job in Singapore is connections, followed by customized and well-targeted applications directly to potential employers.
He should not be frustrated by not receiving replies - Singapore companies never send rejections, so he'll only hear from them if there is a fit.
And also, looking for a job can take months, so patience and perseverance are needed virtues.