The Swedish armed forces at this time consisted of conscripts, led by a mix of conscript NCOs and junior officers and reserve and professional NCOs, technicians or medical personell, junior and senior officers. There were also a small group of "leftover" alotment personell that had been allowed to remain after conscription was introduced 1901, but most were in some kind of technical or administrative role or retired but still in theory on the lists (stories exists of men like these being brought in for celebrations and parties, more or less as mascots up until the early 1970s, being plied with alcohol and food, dressed up in their ancient parade uniforms). The men in the reserve had a small yearly pay and yearly exercises beyond that of the conscript repeat trainings.

Durign the Winter War, the Swedish government, with the full support of the armed forces, allowed conscript, reserve and professional personell to postpone required conscription service or reserve service or resign from their post, with the tacit promise that they would be re-hired when they returned, to serve as volunteers in the Finnish armed forces or in SFK, the Swedish volunteer force in Finland.

Finland's situation during the Winter War was close to desperate, and despite significant aid, especially from Sweden, Finland could never entirely arm all their manpower. In the view of the situation, Finland asked that any volunteers would arrive already trained, uniformed and equipped - since they did not have the time nor the resources to train and equip foreign men due to the situation.

8 260 men were approved for the SFK (727 of them being Norwegian), and a further roughly 500 served in the Finnish army. A further roughly 4 000 had been approved but had not been formed into units when the war ended.

Of those 8 260, 460 were professionals (122 officers and 348 NCOs) and 77 (65 officers and 12 NCOs) reservists.

Many of the officers had already served in the Finnish army during the Finnish Civil War, either as officers of the Finnish army or as volunteers in the Swedish Brigade that served on the white side n the civil war. On eof the most prominent was General Ernst Linder, who commanded the SFK 1939-1940 but had also served the Finnish army during the civil war. Other interesting cases are Captain Viking Tamm, who had served in the Swedish military mission in Ethiopia, created the Oleta Cadet School and briefly commanded a mixed Ethiopian brigade of young cadets and older chitet (an Ethiopian feudal levy) during the Itlaian invasion. Tamm would later rise to become chief of the Swedish army staff.

In line with the Finnish wish for men already trained, the SFK prioritised veterans, including men who had fought in the Finnish Civil War, but also roughly 20 men that had fought in the International Brigades on the Republican side in the Spanish Civil War. According to an interview with Conny Andersson, social democrat and veteran from the International Brigades, he encountered a very small group of Swedes that had fought on Franco's side in SFK!

The men promised that they would be re-hired if they resigned to serve in the Winter War could be reasonably certain the armed forces and the government would keep their promise - many prominent officers in the army, including Linder, had been promised the same thing in 1918 and had seen that promise be fulfilled and their own careers progress as could have been expected before their resignation, or even better due to their experience.

The armed forces and the government would keep their promise and as in 1918, many of the officers and NCOs would like Viking Tamm become prominent senior officers and have a large amount of influence on Swedish army and air doctrine and tactics. Finland had developed its own version of the rotten-schwarm/fighting pair-finger four tactics and had ued it since 1932. Combined with the excellent training of Finnish fighter pilots, this allowed Finland to achieve unprecedented kill ratios in the air against the Soviet Air Force. The Swedish volunteer air unit, F 19, included a third of the active Swedish fighter squadrons at this time and quickly took to the Finnish tactics, and in Spring 1940, the entire Swedish air force switched over from the older vic formation to the newer rotten-schwarm one, which was made official in the June 1940 reoganisation of the air force.

Likewise, the officers and men that served in Finland would have quite some influence on Swedish army doctrine. Sweden adopted a variant of the Finnish long range infiltration and patrol doctrine and motti tactics appears in the Swedish infantry combat manuls of 1940 and onwards. Likewise, you can see some Finnish influence on the Swedish Free War doctrine adopted in 1943.

During the Continuation War, the government and the armed forces did not allow men to resign with the promise to be re-hired and while many still did and were re-hired later, they did not have their time served in the Finnish armed forces counted for their seniority and few if any of them rose to such prominence as Linder and Tamm had. In general, Sweden avoided prosecuting those that illegaly joined other countries' armed forces, with only a scant few examples among the 167 SS volunteers for avoiding conscription.

So, to answer your question, the experience of the men who served in the Swedish Brigade and the SFK was highly valued in the Swedish armed forces, and many of the men who served in those formations rose to become prominent officers in the Swedish armed forces. Their experiences would also influence the doctrines and tactics of the Swedish armed forces, especially the air force. The men who served in the Continuation War were fewer, did so in the face of a much more lukewarm response among the public, one that eventually also influenced the government and the armed forces.

Sources:

När Finlands sak blev min, by Orvar Nilsson.

Det svenska vinterkriget 1939-1940 by Leif Björkman.

Sverige under andra världskriget by Anders Frankson..

Svenskar i krig by Lars Gyllenhaal and Lennart Westberg