Basic question: converting & inflating currencies

Hello everyone!

I'm a graduate student in population & public health but I have an high school/'undergraduate level' economics question for you folks!

I am looking to convert dollar values from various countries & currencies into USD to a common year (for example: 2013). What I have is a bunch of cost of illness estimates for a single disease that were done on a national level for various countries over the course of about 20 years (mainly the US and the UK).

As an example:

$1000 USD (2009) in USA £ 1000 sterling (2008) in UK I want to convert the sterling (UK) value into$ USD in 2013. Converting the dollar-figure estimated in USD to 2013 values is fairly easy from what I understand (I can use an online calculator or look up CPI inflation values manually)... but I am a little confused on how to do the dollar-values from other countries.

Would I:

[Inflate first-convert second]
- Use country-specific CPI values (say UK CPI values, or their equivalents) to inflate 2008 £ figure to 2013 £ and THEN convert to USD using a 'current' conversion factor?

or

[Convert first-inflate second]
- Convert the 2008 £ figure to 2008 USD and then use US CPI value to bring up to 2013 USD value?

Thanks so much for the help!